Self-conjugate vector partitions and the parity of the spt-function

• Autorzy: George E. Andrews , Frank G. Garvan , Jie Liang
• Języki publikacji: EN

Abstrakty

EN

Let spt(n) denote the total number of appearances of the smallest parts in all the partitions of n. Recently, we found new combinatorial interpretations of congruences for the spt-function modulo 5 and 7. These interpretations were in terms of a restricted set of weighted vector partitions which we call S-partitions. We prove that the number of self-conjugate S-partitions, counted with a certain weight, is related to the coefficients of a certain mock theta function studied by the first author, Dyson and Hickerson. As a result we obtain an elementary q-series proof of Ono and Folsom's results for the parity of spt(n). A number of related generating function identities are also obtained.

Kategorie tematyczne

• 11P83: Partitions; congruences and congruential restrictions
• 11F33: Congruences for modular and p -adic modular forms
• 11P84: Partition identities; identities of Rogers-Ramanujan type
• 05A19: Combinatorial identities, bijective combinatorics
• 11P82: Analytic theory of partitions
• 11P81: Elementary theory of partitions
• 05A17: Partitions of integers
• 33D15: Basic hypergeometric functions in one variable, r φ s

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 158
• Numer: 3
• Strony: 199-218

Daty

wydano

2013

Twórcy

autor

George E. Andrews

• Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, U.S.A.

autor

Frank G. Garvan

• Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, U.S.A.

autor

Jie Liang

• Department of Mathematics, University of Florida, Gainesville, FL 32611-8105, U.S.A.

Identyfikatory

DOI

10.4064/aa158-3-1