Inequalities for the overpartition function
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 $n\neq 7$. … 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.
Inequalities for the overpartition function
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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 … 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 , …
WebThe 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. Web19 jan. 2024 · Let denote the overpartition funtion. This paper presents the - -concavity property of by considering a more general inequality of the following form which holds …
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 ] WebIn 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 …
Web15 dec. 2024 · PDF On Dec 15, 2024, Gargi Mukherjee published INEQUALITIES FOR THE OVERPARTITION FUNCTION ARISING FROM DETERMINANT Find, read and …
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], … flashlight books walnut creek caflash light blue tileWeb15 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 … flashlight bodyWeb19 jan. 2024 · [PDF] Inequalities for the overpartition function arising from determinants Semantic Scholar Let p(n) denote the overpartition funtion. This paper presents the 2-logconcavity property of p(n) by considering a more general inequality of the following form Let p(n) denote the overpartition funtion. flashlight bombWebBase 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 ). … flashlight bluetooth beanieWeb26 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 … check for text messagesWeb24 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 … flashlight blueprint