Inequalities for the overpartition function
WebThe proof depends on a result of Engle [6] on the bound of the overpartition function. In this paper, we will provide a combinatorial proof to the Liu-Zhang inequality for overpartition function, which closely follows the proof of the corresponding theorem for ppnq in [1], and the proof method gives an extension of Theorem 1.2. Web17 apr. 2024 · The generating functions which occur in the theory of partitions and functions closely related to them belong to two important classes of functions, namely …
Inequalities for the overpartition function
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Web1 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], … Web13 mei 2024 · Prior to Engel’s work on overpartitions, \(\log \)-concavity of partition function p(n) and its associated inequalities has been studied in a broad spectrum, for …
WebLet p¯(n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} … 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 , …
Web9 mei 2024 · In 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 function obtained by DeSalvo and Pak [ 9 ] and Bessenrodt and Ono [ 2 ]. Web19 jan. 2024 · Inequalities for the overpartition function arising from determinants Gargi Mukherjee Let denote the overpartition funtion. This paper presents the - -concavity property of by considering a more general inequality of the following form which holds for all . Submission history From: Gargi Mukherjee [ view email ]
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 such family of inequalities arises from real rootedness properties of certain polynomials, so called Jensen polynomials which amounts to say the log-concavity property, more …
Web24 mei 2024 · number of inequalities for the overpartition function by considering totally positive matrix of order k kwith k2Z 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. bowler wine importersWeb15 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 $n\neq 7$. … bowler wi post officeWeb15 aug. 2024 · Inequalities for the overpartition function. Edward Y.S. Liu, Helen W.J. Zhang. Let denote the overpartition funtion. Engel showed that for , satisfied the Turán … gullys indoor campingWebpartition function p(n) and its associated inequalities has been studied in a wider spectrum, details can be found in [1], [2], and [5]. Liu and Zhang [11] 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 bowler wineWebBase 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 ). … gully sockWebThe proof depends on a result of Engle[] on the bound of the overpartition function. In this paper, we will provide a combinatorial proof to the Liu-Zhang inequality for overpartition function, which closely follows the proof of the corresponding theorem for p (n) 𝑝 𝑛 p(n) italic_p ( italic_n ) in [], and the proof method gives an extension of Theorem 1.2. gully smartWeb15 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). gullys lake wear port clinton