| Name | kececisquares JSON |
| Version |
0.1.1
JSON |
| download |
| home_page | https://github.com/WhiteSymmetry/kececisquares |
| Summary | Keçeci Binomial Squares (Keçeci Binom Kareleri): The Keçeci Binomial Square is a series of binomial coefficients forming a square region within Khayyam (مثلث خیام), Pascal, Binomial Triangle, selected from a specified starting row with defined size and alignment. |
| upload_time | 2025-08-05 07:45:18 |
| maintainer | Mehmet Keçeci |
| docs_url | None |
| author | Mehmet Keçeci |
| requires_python | >=3.9 |
| license | MIT |
| keywords |
|
| VCS |
 |
| bugtrack_url |
|
| requirements |
No requirements were recorded.
|
| Travis-CI |
No Travis.
|
| coveralls test coverage |
No coveralls.
|
# Keçeci Binomial Squares (Keçeci Binom Kareleri): Keçeci's Arithmetical Square (Keçeci Aritmetik Karesi, Keçeci'nin Aritmetik Karesi)
[](https://badge.fury.io/py/kececisquares)
[](https://opensource.org/licenses/MIT)
[](https://doi.org/10.5281/zenodo.15411670)
[](https://doi.org/10.5281/zenodo.15425855)
[](https://doi.org/10.22541/au.175070836.63624913/v1)
[](https://doi.org/10.48546/workflowhub.datafile.15.1)
[](https://anaconda.org/bilgi/kececisquares)
[](https://anaconda.org/bilgi/kececisquares)
[](https://anaconda.org/bilgi/kececisquares)
[](https://anaconda.org/bilgi/kececisquares)
[](https://opensource.org/)
[](https://kececisquares.readthedocs.io/en/latest)
[](https://www.bestpractices.dev/projects/)
[](https://github.com/WhiteSymmetry/kececisquares/actions/workflows/python_ci.yml)
[](https://codecov.io/gh/WhiteSymmetry/kececisquares)
[](https://kececisquares.readthedocs.io/en/latest/)
[](https://terrarium.evidencepub.io/v2/gh/WhiteSymmetry/kececisquares/HEAD)
[](https://badge.fury.io/py/kececisquares)
[](https://pepy.tech/projects/kececisquares)
[](CODE_OF_CONDUCT.md)
[](https://github.com/astral-sh/ruff)
---
<p align="left">
<table>
<tr>
<td style="text-align: center;">PyPI</td>
<td style="text-align: center;">
<a href="https://pypi.org/project/kececisquares/">
<img src="https://badge.fury.io/py/kececisquares.svg" alt="PyPI version" height="18"/>
</a>
</td>
</tr>
<tr>
<td style="text-align: center;">Conda</td>
<td style="text-align: center;">
<a href="https://anaconda.org/bilgi/kececisquares">
<img src="https://anaconda.org/bilgi/kececisquares/badges/version.svg" alt="conda-forge version" height="18"/>
</a>
</td>
</tr>
<tr>
<td style="text-align: center;">DOI</td>
<td style="text-align: center;">
<a href="https://doi.org/10.5281/zenodo.15411670">
<img src="https://zenodo.org/badge/DOI/10.5281/zenodo.15411670.svg" alt="DOI" height="18"/>
</a>
</td>
</tr>
<tr>
<td style="text-align: center;">License: MIT</td>
<td style="text-align: center;">
<a href="https://opensource.org/licenses/MIT">
<img src="https://img.shields.io/badge/License-MIT-yellow.svg" alt="License" height="18"/>
</a>
</td>
</tr>
</table>
</p>
---
## Description / Açıklama
**Keçeci Binomial Squares (Keçeci Binom Kareleri): Keçeci's Arithmetical Square (Keçeci Aritmetik Karesi, Keçeci'nin Aritmetik Karesi)**:
Keçeci Binomial Squares (Keçeci Binom Kareleri): The Keçeci Binomial Square is a series of binomial coefficients forming a square region within Khayyam (مثلث خیام), Pascal, Binomial Triangle, selected from a specified starting row with defined size and alignment.
Keçeci Binom Karesi, Hayyam (مثلث خیام), Pascal, Binomial üçgeni içinde belirli bir başlangıç satırından itibaren, seçili boyut ve hizalamada bir kare oluşturan binom katsayıları serisidir.
---
## Installation / Kurulum
```bash
conda install bilgi::kececisquares -y
pip install kececisquares
```
https://anaconda.org/bilgi/kececisquares
https://pypi.org/project/kececisquares/
https://github.com/WhiteSymmetry/kececisquares
https://zenodo.org/records/15411671
https://zenodo.org/records/
---
## Usage / Kullanım
### Example
```python
import matplotlib.pyplot as plt
import kececisquares as ks
import math # For math.ceil
# Cell 2: Function to get user input (optional, you can hardcode for simplicity)
def get_user_parameters():
"""Gets parameters from the user."""
print("--- Configure Binomial Triangle Visualization ---")
try:
num_rows = int(input("Enter number of rows for Pascal's/Binomial Triangle (e.g., 7, min: 1): "))
if num_rows < 1:
print("Error: Number of rows must be at least 1.")
return None
practical_max_square_size = math.ceil(num_rows / 2) if num_rows > 1 else 1
square_size_prompt = (f"Enter square size (1-{num_rows}, e.g., 3, "
f"practical max for centered: {practical_max_square_size}): ")
square_size = int(input(square_size_prompt))
if not (1 <= square_size <= num_rows):
print(f"Error: Square size must be between 1 and {num_rows}.")
return None
min_start_row_0idx = max(0, square_size - 1)
max_start_row_0idx = num_rows - square_size
if min_start_row_0idx > max_start_row_0idx:
print(f"A {square_size}x{square_size} square cannot be formed in a triangle of {num_rows} rows.")
return None
start_row_prompt = (f"Enter starting row for the square "
f"(1-indexed, between {min_start_row_0idx + 1} and {max_start_row_0idx + 1}, "
f"e.g., {min_start_row_0idx + 1}): ")
start_row_user = int(input(start_row_prompt))
start_row_0idx = start_row_user - 1
if not (min_start_row_0idx <= start_row_0idx <= max_start_row_0idx):
print(f"Error: Starting row (1-indexed) must be between {min_start_row_0idx + 1} and {max_start_row_0idx + 1}.")
return None
shape_prompt = "Shape type (1: hexagon, 2: square, 3: circle, 4: triangle; default: 1-hexagon): "
shape_choice = input(shape_prompt).strip()
shape_map = {"1": "hexagon", "2": "square", "3": "circle", "4": "triangle"}
shape_type = "hexagon"
if shape_choice == "": print("Defaulting to 'hexagon' (1).")
elif shape_choice in shape_map: shape_type = shape_map[shape_choice]
else: print(f"Invalid shape type. Defaulting to 'hexagon' (1).")
align_prompt = "Square alignment (1: Left, 2: Right, 3: Centered; default: 1-Left): "
align_choice = input(align_prompt).strip()
align_map = {"1": "left", "2": "right", "3": "center"}
alignment = "left"
if align_choice == "": print("Defaulting to 'Left-Aligned' (1).")
elif align_choice in align_map: alignment = align_map[align_choice]
else: print(f"Invalid alignment. Defaulting to 'Left-Aligned' (1).")
fill_prompt = "Fill the square? (1: Yes, 2: No; default: 1-Yes): "
fill_choice = input(fill_prompt).strip()
is_filled = True
if fill_choice == "1": pass
elif fill_choice == "2": is_filled = False
elif fill_choice == "": print("Defaulting to 'Yes' (1).")
else: print(f"Invalid fill choice. Defaulting to 'Yes' (1).")
show_val_prompt = "Show numbers inside shapes? (1: Yes, 2: No; default: 1-Yes): "
show_val_choice = input(show_val_prompt).strip()
show_numbers = True # Varsayılan
if show_val_choice == "1": pass
elif show_val_choice == "2": show_numbers = False
elif show_val_choice == "": print("Defaulting to show numbers (1).")
else: print(f"Invalid choice for showing numbers. Defaulting to show numbers (1).")
return {
"num_rows": num_rows,
"square_size": square_size,
"start_row_0idx": start_row_0idx,
"shape_type": shape_type,
"alignment": alignment,
"is_filled": is_filled,
"show_numbers": show_numbers, # Yeni parametreyi sözlüğe ekle
}
except ValueError:
print("Error: Invalid numerical input.")
return None
except Exception as e:
print(f"An unexpected error occurred during input: {e}")
return None
# Cell 3: Get parameters and run the visualization
params = get_user_parameters()
if params:
print("\n--- Generating Plot ---")
# Call the drawing function from the module
# Pass show_plot=False if you want to manage plt.show() or save the figure later
# We let the module handle plt.show() by default for simplicity here.
fig, ax = ks.draw_kececi_binomial_square(
num_rows_to_draw=params["num_rows"],
square_region_size=params["square_size"],
start_row_index_for_square_0based=params["start_row_0idx"],
shape_to_draw=params["shape_type"],
square_alignment=params["alignment"],
is_square_filled=params["is_filled"],
show_plot=True, # Let the function call plt.show()
show_values=params.get("show_numbers", True) # Yeni parametre, varsayılan True
)
if fig:
print("Plot generated successfully.")
# You can do more with fig and ax here if needed, e.g., fig.savefig("triangle.png")
else:
print("Plot generation failed.")
else:
print("Could not proceed due to invalid parameters.")
```
---
---
---
---
## License / Lisans
This project is licensed under the MIT License. See the `LICENSE` file for details.
## Citation
If this library was useful to you in your research, please cite us. Following the [GitHub citation standards](https://docs.github.com/en/github/creating-cloning-and-archiving-repositories/creating-a-repository-on-github/about-citation-files), here is the recommended citation.
### BibTeX
```bibtex
@misc{kececi_2025_15411670,
author = {Keçeci, Mehmet},
title = {kececisquares},
month = may,
year = 2025,
publisher = {GitHub, PyPI, Anaconda, Zenodo},
version = {0.1.0},
doi = {10.5281/zenodo.15411670},
url = {https://doi.org/10.5281/zenodo.15411670},
}
@misc{kececi_2025_15425855,
author = {Keçeci, Mehmet},
title = {The Keçeci Binomial Square: A Reinterpretation of
the Standard Binomial Expansion and Its Potential
Applications
},
month = may,
year = 2025,
publisher = {Zenodo},
doi = {10.5281/zenodo.15425855},
url = {https://doi.org/10.5281/zenodo.15425855},
}
```
### APA
```
Keçeci, M. (2025). kececisquares [Data set]. WorkflowHub. https://doi.org/10.48546/workflowhub.datafile.15.1
Keçeci, M. (2025). Keçeci's Arithmetical Square. Authorea. June, 2025. https://doi.org/10.22541/au.175070836.63624913/v1
Keçeci, M. (2025). kececisquares. Zenodo. https://doi.org/10.5281/zenodo.15411670
Keçeci, M. (2025). The Keçeci Binomial Square: A Reinterpretation of the Standard Binomial Expansion and Its Potential Applications. https://doi.org/10.5281/zenodo.15425855
```
### Chicago
```
Keçeci, Mehmet. kececisquares [Data set]. WorkflowHub, 2025. https://doi.org/10.48546/workflowhub.datafile.15.1
Keçeci, Mehmet. "Keçeci's Arithmetical Square". Authorea. June, 2025. https://doi.org/10.22541/au.175070836.63624913/v1
Keçeci, Mehmet. "kececisquares". Zenodo, 01 May 2025. https://doi.org/10.5281/zenodo.15411670
Keçeci, Mehmet. "The Keçeci Binomial Square: A Reinterpretation of the Standard Binomial Expansion and Its Potential Applications", 15 Mayıs 2025. https://doi.org/10.5281/zenodo.15425855
```
Raw data
{
"_id": null,
"home_page": "https://github.com/WhiteSymmetry/kececisquares",
"name": "kececisquares",
"maintainer": "Mehmet Ke\u00e7eci",
"docs_url": null,
"requires_python": ">=3.9",
"maintainer_email": "bilginomi@yaani.com",
"keywords": null,
"author": "Mehmet Ke\u00e7eci",
"author_email": "bilginomi@yaani.com",
"download_url": "https://files.pythonhosted.org/packages/a0/e8/d3516445b430d4a40fd95bb9b16fae2bc83b09df496a2d5477a2898b6698/kececisquares-0.1.1.tar.gz",
"platform": null,
"description": "\n# Ke\u00e7eci Binomial Squares (Ke\u00e7eci Binom Kareleri): Ke\u00e7eci's Arithmetical Square (Ke\u00e7eci Aritmetik Karesi, Ke\u00e7eci'nin Aritmetik Karesi)\n\n[](https://badge.fury.io/py/kececisquares)\n[](https://opensource.org/licenses/MIT)\n\n[](https://doi.org/10.5281/zenodo.15411670)\n[](https://doi.org/10.5281/zenodo.15425855)\n\n[](https://doi.org/10.22541/au.175070836.63624913/v1)\n\n[](https://doi.org/10.48546/workflowhub.datafile.15.1)\n\n[](https://anaconda.org/bilgi/kececisquares)\n[](https://anaconda.org/bilgi/kececisquares)\n[](https://anaconda.org/bilgi/kececisquares)\n[](https://anaconda.org/bilgi/kececisquares)\n\n[](https://opensource.org/)\n[](https://kececisquares.readthedocs.io/en/latest)\n\n[](https://www.bestpractices.dev/projects/)\n\n[](https://github.com/WhiteSymmetry/kececisquares/actions/workflows/python_ci.yml)\n[](https://codecov.io/gh/WhiteSymmetry/kececisquares)\n[](https://kececisquares.readthedocs.io/en/latest/)\n[](https://terrarium.evidencepub.io/v2/gh/WhiteSymmetry/kececisquares/HEAD)\n[](https://badge.fury.io/py/kececisquares)\n[](https://pepy.tech/projects/kececisquares)\n[](CODE_OF_CONDUCT.md)\n[](https://github.com/astral-sh/ruff)\n\n---\n\n<p align=\"left\">\n <table>\n <tr>\n <td style=\"text-align: center;\">PyPI</td>\n <td style=\"text-align: center;\">\n <a href=\"https://pypi.org/project/kececisquares/\">\n <img src=\"https://badge.fury.io/py/kececisquares.svg\" alt=\"PyPI version\" height=\"18\"/>\n </a>\n </td>\n </tr>\n <tr>\n <td style=\"text-align: center;\">Conda</td>\n <td style=\"text-align: center;\">\n <a href=\"https://anaconda.org/bilgi/kececisquares\">\n <img src=\"https://anaconda.org/bilgi/kececisquares/badges/version.svg\" alt=\"conda-forge version\" height=\"18\"/>\n </a>\n </td>\n </tr>\n <tr>\n <td style=\"text-align: center;\">DOI</td>\n <td style=\"text-align: center;\">\n <a href=\"https://doi.org/10.5281/zenodo.15411670\">\n <img src=\"https://zenodo.org/badge/DOI/10.5281/zenodo.15411670.svg\" alt=\"DOI\" height=\"18\"/>\n </a>\n </td>\n </tr>\n <tr>\n <td style=\"text-align: center;\">License: MIT</td>\n <td style=\"text-align: center;\">\n <a href=\"https://opensource.org/licenses/MIT\">\n <img src=\"https://img.shields.io/badge/License-MIT-yellow.svg\" alt=\"License\" height=\"18\"/>\n </a>\n </td>\n </tr>\n </table>\n</p>\n\n---\n\n## Description / A\u00e7\u0131klama\n\n**Ke\u00e7eci Binomial Squares (Ke\u00e7eci Binom Kareleri): Ke\u00e7eci's Arithmetical Square (Ke\u00e7eci Aritmetik Karesi, Ke\u00e7eci'nin Aritmetik Karesi)**: \n\nKe\u00e7eci Binomial Squares (Ke\u00e7eci Binom Kareleri): The Ke\u00e7eci Binomial Square is a series of binomial coefficients forming a square region within Khayyam (\u0645\u062b\u0644\u062b \u062e\u06cc\u0627\u0645), Pascal, Binomial Triangle, selected from a specified starting row with defined size and alignment.\n\nKe\u00e7eci Binom Karesi, Hayyam (\u0645\u062b\u0644\u062b \u062e\u06cc\u0627\u0645), Pascal, Binomial \u00fc\u00e7geni i\u00e7inde belirli bir ba\u015flang\u0131\u00e7 sat\u0131r\u0131ndan itibaren, se\u00e7ili boyut ve hizalamada bir kare olu\u015fturan binom katsay\u0131lar\u0131 serisidir.\n\n---\n\n## Installation / Kurulum\n\n```bash\nconda install bilgi::kececisquares -y\n\npip install kececisquares\n```\nhttps://anaconda.org/bilgi/kececisquares\n\nhttps://pypi.org/project/kececisquares/\n\nhttps://github.com/WhiteSymmetry/kececisquares\n\nhttps://zenodo.org/records/15411671\n\nhttps://zenodo.org/records/\n\n---\n\n## Usage / Kullan\u0131m\n\n### Example\n\n```python\nimport matplotlib.pyplot as plt\nimport kececisquares as ks\nimport math # For math.ceil\n\n\n# Cell 2: Function to get user input (optional, you can hardcode for simplicity)\ndef get_user_parameters():\n \"\"\"Gets parameters from the user.\"\"\"\n print(\"--- Configure Binomial Triangle Visualization ---\")\n try:\n num_rows = int(input(\"Enter number of rows for Pascal's/Binomial Triangle (e.g., 7, min: 1): \"))\n if num_rows < 1:\n print(\"Error: Number of rows must be at least 1.\")\n return None\n\n practical_max_square_size = math.ceil(num_rows / 2) if num_rows > 1 else 1\n square_size_prompt = (f\"Enter square size (1-{num_rows}, e.g., 3, \"\n f\"practical max for centered: {practical_max_square_size}): \")\n square_size = int(input(square_size_prompt))\n if not (1 <= square_size <= num_rows):\n print(f\"Error: Square size must be between 1 and {num_rows}.\")\n return None\n\n min_start_row_0idx = max(0, square_size - 1)\n max_start_row_0idx = num_rows - square_size\n if min_start_row_0idx > max_start_row_0idx:\n print(f\"A {square_size}x{square_size} square cannot be formed in a triangle of {num_rows} rows.\")\n return None\n\n start_row_prompt = (f\"Enter starting row for the square \"\n f\"(1-indexed, between {min_start_row_0idx + 1} and {max_start_row_0idx + 1}, \"\n f\"e.g., {min_start_row_0idx + 1}): \")\n start_row_user = int(input(start_row_prompt))\n start_row_0idx = start_row_user - 1\n if not (min_start_row_0idx <= start_row_0idx <= max_start_row_0idx):\n print(f\"Error: Starting row (1-indexed) must be between {min_start_row_0idx + 1} and {max_start_row_0idx + 1}.\")\n return None\n\n shape_prompt = \"Shape type (1: hexagon, 2: square, 3: circle, 4: triangle; default: 1-hexagon): \"\n shape_choice = input(shape_prompt).strip()\n shape_map = {\"1\": \"hexagon\", \"2\": \"square\", \"3\": \"circle\", \"4\": \"triangle\"}\n shape_type = \"hexagon\"\n if shape_choice == \"\": print(\"Defaulting to 'hexagon' (1).\")\n elif shape_choice in shape_map: shape_type = shape_map[shape_choice]\n else: print(f\"Invalid shape type. Defaulting to 'hexagon' (1).\")\n\n align_prompt = \"Square alignment (1: Left, 2: Right, 3: Centered; default: 1-Left): \"\n align_choice = input(align_prompt).strip()\n align_map = {\"1\": \"left\", \"2\": \"right\", \"3\": \"center\"}\n alignment = \"left\"\n if align_choice == \"\": print(\"Defaulting to 'Left-Aligned' (1).\")\n elif align_choice in align_map: alignment = align_map[align_choice]\n else: print(f\"Invalid alignment. Defaulting to 'Left-Aligned' (1).\")\n\n fill_prompt = \"Fill the square? (1: Yes, 2: No; default: 1-Yes): \"\n fill_choice = input(fill_prompt).strip()\n is_filled = True\n if fill_choice == \"1\": pass\n elif fill_choice == \"2\": is_filled = False\n elif fill_choice == \"\": print(\"Defaulting to 'Yes' (1).\")\n else: print(f\"Invalid fill choice. Defaulting to 'Yes' (1).\")\n\n show_val_prompt = \"Show numbers inside shapes? (1: Yes, 2: No; default: 1-Yes): \"\n show_val_choice = input(show_val_prompt).strip()\n show_numbers = True # Varsay\u0131lan\n if show_val_choice == \"1\": pass\n elif show_val_choice == \"2\": show_numbers = False\n elif show_val_choice == \"\": print(\"Defaulting to show numbers (1).\")\n else: print(f\"Invalid choice for showing numbers. Defaulting to show numbers (1).\")\n \n return {\n \"num_rows\": num_rows,\n \"square_size\": square_size,\n \"start_row_0idx\": start_row_0idx,\n \"shape_type\": shape_type,\n \"alignment\": alignment,\n \"is_filled\": is_filled,\n \"show_numbers\": show_numbers, # Yeni parametreyi s\u00f6zl\u00fc\u011fe ekle\n }\n except ValueError:\n print(\"Error: Invalid numerical input.\")\n return None\n except Exception as e:\n print(f\"An unexpected error occurred during input: {e}\")\n return None\n\n# Cell 3: Get parameters and run the visualization\nparams = get_user_parameters()\n\nif params:\n print(\"\\n--- Generating Plot ---\")\n # Call the drawing function from the module\n # Pass show_plot=False if you want to manage plt.show() or save the figure later\n # We let the module handle plt.show() by default for simplicity here.\n fig, ax = ks.draw_kececi_binomial_square(\n num_rows_to_draw=params[\"num_rows\"],\n square_region_size=params[\"square_size\"],\n start_row_index_for_square_0based=params[\"start_row_0idx\"],\n shape_to_draw=params[\"shape_type\"],\n square_alignment=params[\"alignment\"],\n is_square_filled=params[\"is_filled\"],\n show_plot=True, # Let the function call plt.show()\n show_values=params.get(\"show_numbers\", True) # Yeni parametre, varsay\u0131lan True\n )\n\n if fig:\n print(\"Plot generated successfully.\")\n # You can do more with fig and ax here if needed, e.g., fig.savefig(\"triangle.png\")\n else:\n print(\"Plot generation failed.\")\nelse:\n print(\"Could not proceed due to invalid parameters.\")\n```\n---\n\n\n---\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n---\n\n\n---\n\n## License / Lisans\n\nThis project is licensed under the MIT License. See the `LICENSE` file for details.\n\n## Citation\n\nIf this library was useful to you in your research, please cite us. Following the [GitHub citation standards](https://docs.github.com/en/github/creating-cloning-and-archiving-repositories/creating-a-repository-on-github/about-citation-files), here is the recommended citation.\n\n### BibTeX\n\n```bibtex\n@misc{kececi_2025_15411670,\n author = {Ke\u00e7eci, Mehmet},\n title = {kececisquares},\n month = may,\n year = 2025,\n publisher = {GitHub, PyPI, Anaconda, Zenodo},\n version = {0.1.0},\n doi = {10.5281/zenodo.15411670},\n url = {https://doi.org/10.5281/zenodo.15411670},\n}\n\n@misc{kececi_2025_15425855,\n author = {Ke\u00e7eci, Mehmet},\n title = {The Ke\u00e7eci Binomial Square: A Reinterpretation of\n the Standard Binomial Expansion and Its Potential\n Applications\n },\n month = may,\n year = 2025,\n publisher = {Zenodo},\n doi = {10.5281/zenodo.15425855},\n url = {https://doi.org/10.5281/zenodo.15425855},\n}\n```\n\n### APA\n\n```\nKe\u00e7eci, M. (2025). kececisquares [Data set]. WorkflowHub. https://doi.org/10.48546/workflowhub.datafile.15.1\n\nKe\u00e7eci, M. (2025). Ke\u00e7eci's Arithmetical Square. Authorea. June, 2025. https://doi.org/10.22541/au.175070836.63624913/v1\n\nKe\u00e7eci, M. (2025). kececisquares. Zenodo. https://doi.org/10.5281/zenodo.15411670\n\nKe\u00e7eci, M. (2025). The Ke\u00e7eci Binomial Square: A Reinterpretation of the Standard Binomial Expansion and Its Potential Applications. https://doi.org/10.5281/zenodo.15425855\n\n```\n\n### Chicago\n```\nKe\u00e7eci, Mehmet. kececisquares [Data set]. WorkflowHub, 2025. https://doi.org/10.48546/workflowhub.datafile.15.1\n\nKe\u00e7eci, Mehmet. \"Ke\u00e7eci's Arithmetical Square\". Authorea. June, 2025. https://doi.org/10.22541/au.175070836.63624913/v1\n\nKe\u00e7eci, Mehmet. \"kececisquares\". Zenodo, 01 May 2025. https://doi.org/10.5281/zenodo.15411670\n\nKe\u00e7eci, Mehmet. \"The Ke\u00e7eci Binomial Square: A Reinterpretation of the Standard Binomial Expansion and Its Potential Applications\", 15 May\u0131s 2025. https://doi.org/10.5281/zenodo.15425855\n\n```\n",
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