Web23 feb. 2016 · Abstract. We prove that the overpartition function \overline {p} (n) is log-concave for all n\ge 2 . The proof is based on Sills-Rademacher-type series for \overline … Webnumber of inequalities for the overpartition function by considering totally positive matrix of order k ×k with k ∈ Z≥2, described in Problem 4.1. 2. Inequality for p(n) and its consequences The principal aim of this section is to construct the machinery in order to prove Theorem 1.6, the primary objective of this paper.
Title: Inequalities for the overpartition function arising from ... - arXiv
Web1 aug. 2024 · In this paper, we show the Laguerre inequality of order 2 is true for the partition function, the overpartition function, the Bernoulli numbers, the derangement numbers, the Motzkin numbers, the Fine numbers, the Franel numbers and the Domb numbers. Keywords Partition function Turán inequality of order m The Hardy … Web31 mrt. 2024 · An inequality is obtained for the sequence Δ2logp¯ (n-1)/ ( n-1)αn- 1 which states that log (1+3π4n5/2-11+5αn11/4) motor paint shop
Inequalities for higher order differences of the logarithm of the ...
Web1 aug. 2024 · Wang, Xie and Zhang [41] proved the positivity of finite differences of the overpartition function and gave an upper bound for Δ r p ¯ (n) and Δ r log p ¯ (n). Liu and Zhang [32] showed that the Turán inequality of order 2 is true for p ¯ (n). Now we will prove the overpartition function satisfies the Laguerre inequality of order 2 ... Web15 dec. 2024 · Inequalities Kloosterman sums Overpartitions 1. Introduction and statement of results 1.1. Motivation A partitionof a positive integer nis a non-increasing sequence of positive integers (called parts), usually written as a sum, which add up to n. The number of partitions of nis denoted by p(n). WebInequalities for the Overpartition Function Edward Y.S. Liu1 and Helen W.J. Zhang2 1Center for Combinatorics, LPMC Nankai University, Tianjin 300071, P.R. China 2Center for … motorpal injection pump service manual