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

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

Acta Arithmetica

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,...

Some debts I owe.

Andrews, George E. (1999)

Séminaire Lotharingien de Combinatoire [electronic only]

Some interpretations of the ( k , p ) -Fibonacci numbers

Natalia Paja, Iwona Włoch (2021)

Commentationes Mathematicae Universitatis Carolinae

In this paper we consider two parameters generalization of the Fibonacci numbers and Pell numbers, named as the ( k , p ) -Fibonacci numbers. We give some new interpretations of these numbers. Moreover using these interpretations we prove some identities for the ( k , p ) -Fibonacci numbers.

Some new transformations for Bailey pairs and WP-Bailey pairs

James Mc Laughlin (2010)

Open Mathematics

We derive several new transformations relating WP-Bailey pairs. We also consider the corresponding transformations relating standard Bailey pairs, and as a consequence, derive some quite general expansions for products of theta functions which can also be expressed as certain types of Lambert series.

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