A PROOF OF XIN–ZHANG’S TRIDIAGONAL DETERMINANT CONJECTURE

Abstract

Abstract We confirm a recent conjecture of Xin and Zhang [‘A variation of the Morris constant term’, Preprint, 2024, arXiv:2409.14356v2], which establishes a simple product formula for the characteristic polynomial of an ( n − 1 ) × ( n − 1 ) $(n-1) \times (n-1)$ left parenthesis n minus 1 right parenthesis times left parenthesis n minus 1 right parenthesis tridiagonal matrix. This characteristic polynomial arises from a recurrence relation that enumerates n × n $n \times n$ n times n nonnegative integer matrices with all row and column sums equal to t , also called the Ehrhart polynomial of the n th Birkhoff polytope.