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Simple Cayley permutations
Abstract
We propose a notion of simplicity for Cayley permutations that is compatible with inflation and agrees, under a natural relational encoding, with indecomposability in the sense of Schmerl and Trotter. We establish a substitution decomposition analogous to that of permutations, in which the components are modules of the associated relational structure. We use it to enumerate simple Cayley permutations as well as simple restricted growth functions.
Related
- Prime-valent Symmetric Cayley Graphs of Characteristically Simple Groups
- Automorphism groups of Cayley graphs on almost simple groups with normal connection sets
- On 2-Arc-Transitive Cayley Graphs of Nonabelian Characteristically Simple Groups
- Minimal Cayley graphs with large chromatic number
- A Short Proof of Zhang's Conjecture on Stack-Sortable Permutations
BibTeX
@misc{cerbai2026simple,
title = {{Simple Cayley permutations}},
author = {Giulio Cerbai and Anders Claesson},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.19078},
eprint = {2609.19078},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19078},
}
RIS
TY - UNPB
TI - Simple Cayley permutations
AU - Giulio Cerbai
AU - Anders Claesson
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2609.19078
UR - https://arxiv.org/abs/2609.19078
AB - We propose a notion of simplicity for Cayley permutations that is compatible with inflation and agrees, under a natural relational encoding, with indecomposability in the sense of Schmerl and Trotter. We establish a substitution decomposition analogous to that of permutations, in which the components are modules of the associated relational structure. We use it to enumerate simple Cayley permutations as well as simple restricted growth functions.
ER -