2024/10/04 by Matthias Beck, Danai Deligeorgaki, Beck, Matthias +1
Computer Science · Engineering · Mathematics · #Benford’s Law and Fraud Detection #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2410.03245
openalex publication_date 2024/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A permutation of the multiset \1m,2m,…,nm\ is a \em canon permutation if the subsequence formed by the jth copy of each element of [n]:=\1,2,…,n\ is identical for all j∈[m]. Canon permutations were introduced by Elizalde and are motivated by pattern-avoiding concepts such as (quasi-)Stirling permutations. He proved that the descent polynomial of canon permutations exhibits a surprising product structure; as a further consequence, it is palindromic. Our goal is to understand canon permutations from the viewpoint of Stanley's (P,ω)-partitions, along the way generalizing Elizalde's definition and results. We start with a labeled poset P and extend it in a natural way to canon labelings of the product poset P × [n]. The resulting descent polynomial has a product structure which arises naturally from the theory of (P,ω)-partitions and simplifies existing proofs. When P is graded, this theory also implies palindromicity. We include results on weak descent polynomials, an amphibian construction between canon permutations and multiset permutations, giving rise to dissonant canon permutations, as well as γ-positivity and interpretations of descent polynomials of canon permutations.