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Bringmann, Kathrin, Jennings-Shaffer, Chris and Mahlburg, Karl (2021). The asymptotic distribution of the rank for unimodal sequences. J. Number Theory, 229. S. 444 - 463. SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE. ISSN 1096-1658

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Abstract

We study the asymptotic behavior of the rank statistic for unimodal sequences. We use analytic techniques involving asymptotic expansions in order to prove asymptotic formulas for the moments of the rank. Furthermore, when appropriately normalized, the values of the unimodal rank asymptotically follow a logistic distribution. We also prove similar results for Durfee unimodal sequences and semi-strict unimodal sequences, with the only major difference being that the (normalized) rank for semistrict unimodal sequences has a distributional limit of a point mass probability distribution. (c) 2020 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Bringmann, Kathrin UNSPECIFIED UNSPECIFIED UNSPECIFIED Jennings-Shaffer, Chris UNSPECIFIED UNSPECIFIED UNSPECIFIED Mahlburg, Karl UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-576680
DOI:	10.1016/j.jnt.2020.11.016
Journal or Publication Title:	J. Number Theory
Volume:	229
Page Range:	S. 444 - 463
Date:	2021
Publisher:	ACADEMIC PRESS INC ELSEVIER SCIENCE
Place of Publication:	SAN DIEGO
ISSN:	1096-1658
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language CONCAVE; THEOREM; STACKS Multiple languages Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/57668