Congruences involving generalized Frobenius partitions.

Sellers, James

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Congruences involving F-partition functions.

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Another smallest part function related to Andrews' spt function

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We offer some relations and congruences for two interesting spt-type functions, which together form a relation to Andrews' spt function.

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Schreier-Zassenhaus theorem for algebras. II

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

George E. Andrews, Frank G. Garvan, Jie Liang (2013)

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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...