Exotic Bailey–Slater SPT-functions I: Group A
نویسندگان
چکیده
منابع مشابه
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 known previously for sufficiently large n and...
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In a recent paper, Andrews, Dixit, and Yee introduced a new spt-type function spt ω (n), which is closely related to Ramanujan’s third order mock theta function ω(q). Garvan and Jennings-Shaffer introduce a crank function which explains congruences for spt ω (n). In this note, we study asymptotic behavior of this crank function and confirm a positivity conjecture of the crank asymptotically. We...
متن کاملGeneralized Higher Order Spt-functions
We give a new generalization of the spt-function of G.E. Andrews, namely Sptj(n), and give its combinatorial interpretation in terms of successive lower-Durfee squares. We then generalize the higher order spt-function sptk(n), due to F.G. Garvan, to jsptk(n), thus providing a two-fold generalization of spt(n), and give its combinatorial interpretation.
متن کاملExotic Bailey-slater Spt-functions Ii: Hecke-rogers-type Double Sums and Bailey Pairs from Groups A, C, E
We continue to investigate spt-type functions that arise from Bailey pairs. We prove simple Ramanujan type congruences for these functions which can be explained by a spt-crank-type function. The spt-crank-type functions are constructed by adding an extra variable z into the generating functions. We find these generating functions to have interesting representations as either infinite products ...
متن کاملSoft asymptotics for generalized spt-functions
We derive a leading order asymptotic for the difference between the second moments of Garvan’s generalized rank statistics. The approach uses Dixit and Yee’s combinatorial interpretation of the difference and soft probabilistic techniques to deal with random partitions.
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2017
ISSN: 0001-8708
DOI: 10.1016/j.aim.2016.09.034