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Asymptotic formulae for partition ranks

Jehanne Dousse, Michael H. Mertens (2015)

Acta Arithmetica

Using an extension of Wright's version of the circle method, we obtain asymptotic formulae for partition ranks similar to formulae for partition cranks which where conjectured by F. Dyson and recently proved by the first author and K. Bringmann.

BG-ranks and 2-cores.

Chen, William Y.C., Ji, Kathy Q., Wilf, Herbert S. (2006)

The Electronic Journal of Combinatorics [electronic only]

Calcolo della funzione di partizione di Kostant

Stefano Capparelli (2003)

Bollettino dell'Unione Matematica Italiana

Forniamo un calcolo esplicito della funzione di partizione di Kostant per algebre di Lie complesse di rango 2 . La tecnica principale consiste nella riduzione a casi più semplici ed all'uso di funzioni generatrici.

Combinatorial interpretations for identities using chromatic partitions

Mateus Alegri, Wagner Ferreira Santos, Samuel Brito Silva (2021)

Czechoslovak Mathematical Journal

We provide combinatorial interpretations for three new classes of partitions, the so-called chromatic partitions. Using only combinatorial arguments, we show that these partition identities resemble well-know ordinary partition identities.

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