Higher order spt-functions
Copyright policy )Higher order spt-functions
Andrews' spt-function can be written as the difference between the second symmetrized crank and rank moment functions. Using the machinery of Bailey pairs a combinatorial interpretation is given for the difference between higher order symmetrized crank and rank moment functions. This implies an inequality between crank and rank moments that was only know previously for sufficiently large n and fixed order. This combinatorial interpretation is in terms of a weighted sum of partitions. A number of congruences for higher order spt-functions are derived.
21 pages (previous version was 19 pages), added reference to Andrews and Rose's recent paper, MacMahon's paper and OEIS, changed some wording
- University of Florida United States
- University of Florida United States
- Florida State University United States
Mathematics(all), Partitions, quasimodular forms, 11P82, 11P83, 05A17, 11F33, 33D15, congruences, Bailey pair, Congruences, rank moments, Andrewsʼ spt-function, Basic hypergeometric functions in one variable, \({}_r\phi_s\), primary, FOS: Mathematics, Mathematics - Combinatorics, Number Theory (math.NT), Quasimodular forms, Crank moments, Mathematics - Number Theory, crank moments, Congruences for modular and \(p\)-adic modular forms, Partitions; congruences and congruential restrictions, Baileyʼs Lemma, Bailey's lemma, Andrews' spt-function, partitions, Rank moments, Analytic theory of partitions, Combinatorics (math.CO), secondary
Mathematics(all), Partitions, quasimodular forms, 11P82, 11P83, 05A17, 11F33, 33D15, congruences, Bailey pair, Congruences, rank moments, Andrewsʼ spt-function, Basic hypergeometric functions in one variable, \({}_r\phi_s\), primary, FOS: Mathematics, Mathematics - Combinatorics, Number Theory (math.NT), Quasimodular forms, Crank moments, Mathematics - Number Theory, crank moments, Congruences for modular and \(p\)-adic modular forms, Partitions; congruences and congruential restrictions, Baileyʼs Lemma, Bailey's lemma, Andrews' spt-function, partitions, Rank moments, Analytic theory of partitions, Combinatorics (math.CO), secondary
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).52 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!