The asymptotic distribution of the rank for unimodal sequences

DOI10.1016/j.jnt.2020.11.016zbMath1480.11129arXiv1910.10790OpenAlexW3118068154WikidataQ114157129 ScholiaQ114157129MaRDI QIDQ1981611

Chris Jennings-Shaffer, Karl Mahlburg, Kathrin Bringmann

Publication date: 6 September 2021

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.10790

zbMATH Keywords

asymptoticsdistributionsmodular formsinteger partitionsprobabilistic methodsmock modular formsunimodal sequences

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Forms of half-integer weight; nonholomorphic modular forms (11F37) Analytic theory of partitions (11P82)

Related Items (9)

Limiting Betti distributions of Hilbert schemes on n points ⋮ On the number of parts in congruence classes for partitions into distinct parts ⋮ Taylor coefficients of false Jacobi forms and ranks of unimodal sequences ⋮ Limit shapes for unimodal sequences ⋮ Eventual log-concavity of \(k\)-rank statistics for integer partitions ⋮ Unexpected biases between congruence classes for parts in \(k\)-indivisible partitions ⋮ Unimodality of the Andrews-Garvan-Dyson cranks of partitions ⋮ Asymptotic distribution of odd balanced unimodal sequences with rank congruent to \(a\) modulo \(c\) ⋮ Asymptotics for the twisted eta-product and applications to sign changes in partitions

Cites Work

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• Log-concavity of the partition function
• Ramanujan's ``lost notebook. IV: Stacks and alternating parity in partitions
• Ramanujan-type partial theta identities and rank differences for special unimodal sequences
• On the asymptotic behavior of unimodal rank generating functions
• Sur les entiers n pour lesquels il y à beaucoup de groupes abéliens d'ordre \(n\)
• Concave and convex compositions
• Asymptotic formulas for stacks and unimodal sequences
• A Tauberian theorem for partitions
• Taylor coefficients of mock-Jacobi forms and moments of partition statistics
• New Combinatorial Interpretations of Ramanujan's Partition Congruences Mod 5,7 and 11
• Dyson’s crank of a partition
• Note on a partition limit theorem for rank and crank
• Jensen polynomials for the Riemann zeta function and other sequences
• Peak positions of strongly unimodal sequences
• The rank of a unimodal sequence and a partial theta identity of Ramanujan
• STACKS (II)
• A Family of Combinatorial Identities
• On a Tauberian theorem of Ingham and Euler-Maclaurin summation

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