DOI: 10.1017/s0004972726101993 ISSN: 0004-9727
A PROOF OF XIN–ZHANG’S TRIDIAGONAL DETERMINANT CONJECTURE
JIAQIANG HU, CHEN ZHANG 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.