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MacMahon's partition analysis XI: Broken diamonds and modular forms

100%

Andrews G., Paule P.

Acta Arithmetica

2007

tom 126

nr 3

281-294

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

81%

Andrews G., Garvan F., Liang J.

Acta Arithmetica

2013

tom 158

nr 3

199-218

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.

Ograniczanie wyników

2 Acta Arithmetica

2 Andrews G.

1 Garvan F.

1 Liang J.

1 Paule P.

1 2013

1 2007

Wyniki wyszukiwania

MacMahon's partition analysis XI: Broken diamonds and modular forms

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