Séminaire Lotharingien de Combinatoire, 78B.66 (2017), 12 pp.
The Method of Weighted Words Revisited
Alladi and Gordon introduced the method of weighted words in 1993 to
prove a refinement and generalisation of Schur's partition
identity. Together with Andrews, they later used it to refine
Capparelli's and Göllnitz's identities too. In this paper, we present
a new variant of this method, which can be used to study more
complicated partition identities, and apply it to prove refinements
and generalisations of three partition identities. The first one,
Siladić's theorem (2002), comes from vertex operator algebras. The
second one, a conjectural identity of Primc (1999), comes from crystal
base theory. The last one is a very general identity about coloured
overpartitions which generalises and unifies several generalisations
of Schur's theorem due to Alladi-Gordon, Andrews, Corteel-Lovejoy,
Lovejoy and the author.
Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.
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