Year: 2026
Type: preprint
Abstract: We prove that every hereditary Cayley permutation class with finitely many simple members has a finite basis and an algebraic generating function. We first show that every simple Cayley permutation of length at least two contains a simple pattern obtained by deleting one or two letters, and that the only exceptional Cayley permutations are the simple parallel alternations and their symmetries. We then characterize substitution-closed classes by the simplicity of their basis elements and show that classes with finitely many simple members are partially well ordered. Given the simple members and the basis of such a class, we construct a finite system of functional equations and compute an annihilating polynomial.
Source: arXiv (Cornell University)
Authors: Cerbai, Giulio, Claesson, Anders
Institution: University of Iceland
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223337768