Proof of the Kresch-Tamvakis Conjecture
Number Theory
2023-09-19 v1 Algebraic Geometry
Classical Analysis and ODEs
Combinatorics
Abstract
In this paper we resolve a conjecture of Kresch and Tamvakis. Our result is the following. Theorem: For any positive integer and any integers , the absolute value of the following hypergeometric series is at most 1: \begin{equation*} {_4F_3} \left[ \begin{array}{c} -i, \; i+1, \; -j, \; j+1 \\ 1, \; D+2, \; -D \end{array} ; 1 \right]. \end{equation*} To prove this theorem, we use the Biedenharn-Elliott identity, the theory of Leonard pairs, and the Perron-Frobenius theorem.
Keywords
Cite
@article{arxiv.2309.08869,
title = {Proof of the Kresch-Tamvakis Conjecture},
author = {John S. Caughman and Taiyo S. Terada},
journal= {arXiv preprint arXiv:2309.08869},
year = {2023}
}