Hamza.Yesilyurt

Affiliation: Bilkent University

Title Of Talk: Shifted Partition Identities with Distinct Parts

Abstract: Shifted partition identities are equalities of the form p(S, n) = p(T, n – a), for n ? a, where p(S, n) counts partitions of n with parts taken from a set S. The study began with Andrews in 1987. Soon after, Alladi introduced related identities involving partitions into distinct parts, showing important parallels with the shifted case. Garvan later discovered many more shifted identities, greatly expanding the scope of the subject. In this talk, we review the development of shifted partition identities from their origins to later advances, and we present new identities and recent developments that continue to enrich the interplay between partition theory and theta functions.

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