Inequalities for the overpartition function
WebBase case: It can be verified that the inequality holds for n = 4 (a = 3, b = 1 n=4(a=3,b=1 italic_n = 4 ( italic_a = 3 , italic_b = 1 or a = 2, b = 2) a=2,b=2) italic_a = 2 , italic_b = 2 ). … 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)
Inequalities for the overpartition function
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Web24 mei 2024 · OVERPARTITION FUNCTION AND APROBLEMOFWANG-XIE-ZHANG GargiMukherjee DK-ReportNo. 2024-07 05 2024 A–4040LINZ ... proved a family of inequalities for the overpartition function. Chen, Guo and Wang [3] introduced the notion of ratio log-convexity of a sequence and established that ratio log-convexity implies log … 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 …
Web21 jun. 2024 · In this talk, we shall study inequalities for the overpartition function, a generalization of the partition function. The central theme of this talk is how the study of … Web15 aug. 2024 · Inequalities for the overpartition function. Let $$\overline {p} (n)$$ p ¯ ( n ) denote the overpartition function. Engel showed that for $$n\ge 2$$ n ≥ 2 , …
Web15 aug. 2024 · Extending the partition function multiplicatively to a function on partitions, we show that it has a unique maximum at an explicitly given partition for any $n\neq 7$. … 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 …
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.
Web6 sep. 2024 · Abstract. Let denote the number of overpartitions of n into odd parts. In this paper, we provide a complete characterization of Ramanujan-type congruences modulo 8 for the overpartition function ... le fort wagnerWeb1 apr. 2024 · Prior to Engel's work on overpartitions, log-concavity of partition function p (n) and its associated inequalities has been studied in a wider spectrum, can be found in [1], … lefort\u0027s seafoodWeb1 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 ... le fosburyWebIn this paper, we prove some inequalities for the overpartition function. One of main results of this paper is the following theorem analogous to these inequalities for the partition … le forum university of maineWebThe overpartition function, a generalization of the partition function, falls into the domain of number theory and combinatorics, studied through the lens of asymptotic enumeration in … le forum orthoWeb21 jan. 2016 · To do so we make improvements on the current state of the overpartition rank function in terms of harmonic Maass forms by giving simple formulas for the the transformations under as well as... le fou aloysius bertrandWeb26 jun. 2024 · We study the partition rank function N ( r , t ; n ), the number of partitions with rank congruent to r modulo t . We first show that it is monotonic in n above a given bound, and then show that it… Expand 15 Highly Influential PDF View 4 excerpts Inequalities for the overpartition function Edward Y. S. Liu, Helen W. J. Zhang … le fotobooth