Higher Order SPT-Functions

By Frank G. Garvan. 2010

101 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Applied Mathematics, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/bb48ba6518df5851de1712c1803b6a0a80d7f1ec

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In Algebra and Number Theory

In Applied Mathematics

In Discrete Mathematics and Combinatorics

Citations in the corpus

Taylor coefficients of mock-Jacobi forms and moments of partition statistics (2014, background): “In particular, the rank moments were related to the crank moments through Atkin and Garvan’s rank-crank PDE [5].”
Asymptotic inequalities for positive crank and rank moments (2012, background): “14) proceeds by finding an alternative description of osptr(N) as a combinatorial counting function that, interestingly, is not a generalization of Garvan’s higher spt-functions in [25].”
Partitions associated with the Ramanujan/Watson mock theta functions ω(q), ν(q)and ϕ(q) (2015, background): “For generalizations and analogues of spt(n), we refer the reader to [12, 18, 20, 23, 27, 28].”