Arndt and Carlitz Compositions

Fuente: arXiv
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Main Authors: Hopkins, Brian, Tangboonduangjit, Aram
Format: Preprint
Published: 2025
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author Hopkins, Brian
Tangboonduangjit, Aram
author_facet Hopkins, Brian
Tangboonduangjit, Aram
contents Carlitz considered integer compositions in which adjacent parts must be unequal. Arndt recently initiated the study of restricted compositions based on conditions applied to certain pairs of parts rather than to individual parts. Here, we combine and generalize these notions, establishing enumeration results using both combinatorial proofs and generating functions. Motivations for our generalizations include the gap-free compositions studied by Hitczenko and Knopfmacher and the Rogers-Ramanujan integer partitions.
format Preprint
id arxiv_https___arxiv_org_abs_2512_12354
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Arndt and Carlitz Compositions
Hopkins, Brian
Tangboonduangjit, Aram
Combinatorics
Number Theory
05A19 (Primary) 05A17, 05A15 (Secondary)
Carlitz considered integer compositions in which adjacent parts must be unequal. Arndt recently initiated the study of restricted compositions based on conditions applied to certain pairs of parts rather than to individual parts. Here, we combine and generalize these notions, establishing enumeration results using both combinatorial proofs and generating functions. Motivations for our generalizations include the gap-free compositions studied by Hitczenko and Knopfmacher and the Rogers-Ramanujan integer partitions.
title Arndt and Carlitz Compositions
topic Combinatorics
Number Theory
05A19 (Primary) 05A17, 05A15 (Secondary)
url https://arxiv.org/abs/2512.12354