The Insertion Encoding of Restricted Growth Functions

Bean, C, Bell, PC ORCID: 0000-0003-2620-635X and Ollson, A (2026) The Insertion Encoding of Restricted Growth Functions. Annals of Combinatorics. ISSN 0218-0006

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Abstract

We adapt the vertical and horizontal insertion encodings of Cayley permutations to enumerate restricted growth functions, which are in bijection with unordered set partitions. For both insertion encodings, we fully classify the classes for which these languages are regular. For the horizontal insertion encoding, we also prove that the conditions to be regular are the same for restricted growth functions of matchings.

Item Type:	Article
Uncontrolled Keywords:	Restricted growth functions; Pattern avoidance; Insertion encoding; Regular languages; Set partitions; 4904 Pure Mathematics; 49 Mathematical Sciences; 0101 Pure Mathematics; 0802 Computation Theory and Mathematics; Computation Theory & Mathematics; 4901 Applied mathematics; 4904 Pure mathematics
Subjects:	Q Science > QA Mathematics
Divisions:	Computer Science and Mathematics
Publisher:	Springer
Date of acceptance:	29 May 2026
Date of first compliant Open Access:	22 September 2026
Date Deposited:	22 Sep 2026 08:15
Last Modified:	22 Sep 2026 08:15
DOI or ID number:	10.1007/s00026-026-00832-y
URI:	https://researchonline.ljmu.ac.uk/id/eprint/29487

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