Laguerre inequalities and determinantal inequalities for the finite difference of the partition functions

2023/12/18 by Yang, Eve Y. Y.
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2312.10909

Abstract

The paper aims to establish the Turán inequalities, the Laguerre inequalities (order 2), and the determinantal inequalities (order 3) for Δp(n) and Δp(n), where Δf(n) is the first-order forward difference of a sequence f(n). The functions p(n) and p(n) denote the partition function and overpartition function, respectively. Conjectures for thresholds of Laguerre inequalities (order m) and positivity of m-order determinants are proposed, extending to Δ^k p(n) and Δ^k p(n), with 1 ≤ m ≤ 11 and 1 ≤ k ≤ 5.

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