Determinants of matrices related to the Pascal triangle

TL;DR

This paper proves a property of Pascal matrices modulo 2, showing that certain sub-matrices have determinants of ±1, confirming a conjecture from 1999.

Contribution

It establishes a mathematical property of Pascal matrices modulo 2, confirming a conjecture about determinants of specific sub-matrices.

Findings

Sub-matrices on the borders have determinants of ±1

Confirms M. Levin's 1999 assertion

Enhances understanding of Pascal matrix properties

Abstract

In this note we prove an assertion made by M. Levin in 1999: the Pascal matrix modulo 2 has the property that each of the square sub-matrices laying on the upper border or on the left border has determinants, computed in $\mathbb{Z}$, equal to 1 or -1.