Séminaire Lotharingien de Combinatoire, 91B.3 (2024), 12 pp.
Alessandro Iraci, Philippe Nadeau and Anna Vanden Wyngaerd
Smirnov Words and the Delta Conjectures
Abstract.
We provide a combinatorial interpretation for the symmetric function
ΘekΘel∇en-k-l
|t=0
in terms of
Smirnov words, which are words where adjacent letters are
distinct. The motivation for this work is the study of a diagonal
coinvariant ring with one set of commuting and two sets of
anti-commuting variables, whose Frobenius characteristic is
conjectured to be the symmetric function in question. It is intimately
related to the two Delta conjectures, as our work is a step towards a
unified formulation of these.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
The following versions are available: