Work

A Proof of Xin–zhang’s Tridiagonal Determinant Conjecture

Year: 2026

Type: article

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.

Source: Bulletin of the Australian Mathematical Society

DOI: 10.1017/s0004972726101993

Authors: JIAQIANG HU, CHEN ZHANG

Institution: Nankai University

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,550

Funders: Capital Normal University, China Postdoctoral Science Foundation, Nankai University