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arXiv · 2509.20521

Scaled Arndt Compositions

Brian Hopkins·Augustine Munagi
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Abstract

Integer compositions restricted by inequalities on certain pairs of parts were first considered by Jörg Arndt in 2013 and several variations have been studied recently. Here we consider a broad two-parameter generalization that scales the defining relation. We connect these to compositions restricted to parts from certain congruence classes and establish the recurrence relations satisfied by the related counting sequences. This provides new combinatorial interpretations to several documented integer sequences and also simple unrecorded sequences. We conclude with suggestions for further study.

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Brian Hopkins, Augustine Munagi. 2025-09-24. Scaled Arndt Compositions. https://arxiv.org/abs/2509.20521

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