Inequalities for the overpartition function
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 ]. Web24 mei 2024 · OVERPARTITION FUNCTION GargiMukherjee DK-ReportNo. 2024-05 05 2024 A–4040LINZ, ALTENBERGERSTRASSE69, AUSTRIA Supportedby ... function p(n) and its associated inequalities has been studied in a broad spectrum, for example see [1], [2], and [5]. Following the same line of studies, ...
Inequalities for the overpartition function
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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 … Webpartition 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
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) 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 …
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. 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 , …
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.
Web26 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 … as加名词做什么成分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 … as句首引导什么从句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 … as医学上心血管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 … as化学元素周期表WebA host of inequalities for overpartition function, see Corollaries 1.4-1.11, appear as a special case of the theorems, similar to the partition ones as discussed before. The primary objective of this paper is to exploit the proof of Theorem 1.2, so that one can bring in all the proofs of Corollaries 1.4-1.11 under a unique as合材 到着温度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 ... as合材 出荷温度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 $n\neq 7$. … as合材 到着温度 管理