2023/12/06 by Alessandro Iraci, Iraci, Alessandro, Philippe Nadeau +3 · 1 citation
Computer Science · Mathematics · #05E05 #05E10 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2312.03956
openalex publication_date 2023/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We provide a combinatorial interpretation of the symmetric function .ΘekΘel∇ en-k-l|t=0 in terms of segmented Smirnov words. 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. Furthermore, this function is related to the Delta conjectures. Our work is a step towards a unified formulation of the two versions, as we prove a unified Delta theorem at t=0.