Companions to the Andrews-Gordon partition identities (Jehanne Dousse, UNIGE)

07.11.2023 10:30

A partition of a positive integer n is a non-increasing sequence of positive integers, called parts, whose sum is n. A partition identity is a theorem stating that for all n, the number of partitions of n satisfying some conditions (often congruence conditions on the parts) equals the number of partitions of n satisfying some other conditions (often difference conditions between the parts). The Andrews-Gordon identities, which generalise the Rogers-Ramanujan identities, are among the most famous and widely studied partition identities. Using techniques from commutative algebra, Pooneh Afsharijoo conjectured in 2020 a companion to these identities (i.e. a partition identity with the same congruence conditions but other difference conditions). In this talk, we will explain the origins of this conjecture and show how it can be proved using Young diagrams, a graphical representation of integer partitions.

This is joint work with Pooneh Afsharijoo, Frédéric Jouhet and Hussein Mourtada.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Tuesday 07.11.2023, Séminaire "Groupes et Géométrie"

entrée libre