论与帕斯卡三角形有关的矩阵行列式

Pub Date : 2024-06-18 DOI:10.1007/s10998-024-00581-6

Martín Mereb

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摘要

我们证明了对称帕斯卡三角形矩阵 modulo 2 具有这样的性质，即位于上边界或左边界的每个正方形子矩阵的行列式，在 \({\mathbb {Z}}\) 中计算，都等于 1 或 \(-1\)。此外，我们还给出了在具有有限单元组的交换环上帕斯卡样（n 次 m\ ）矩阵的确切数目。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On determinants of matrices related to Pascal’s triangle

We prove that the symmetric Pascal triangle matrix modulo 2 has the property that each of the square sub-matrices positioned at the upper border or on the left border has determinant, computed in \({\mathbb {Z}}\), equal to 1 or \(-1\). Furthermore, we give the exact number of Pascal-like \(n \times m\) matrices over a commutative ring with finite group of units.

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