Asymptotics, Turán inequalities, and the distribution of the BG-rank and 2-quotient rank of partitions

2022/03/01 by Andrew Baker, Joshua Males, Baker, Andrew +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2203.00747

openalex publication_date 2022/03/01 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

Let j,n be even positive integers, and let p_j(n) denote the number of partitions with BG-rank j, and p_j(a,b;n) to be the number of partitions with BG-rank j and 2-quotient rank congruent to a \pmodb. We give asymptotics for both statistics, and show that p_j(a,b;n) is asymptotically equidistributed over the congruence classes modulo b. We also show that each of p_j(n) and p_j(a,b;n) asymptotically satisfy all higher-order Turán inequalities.

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