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arXiv · 2603.11934

Decoding universal cycles for t-subsets and t-multisets by decoding bounded-weight de Bruijn sequences

Daniel Gabric·Wazed Imam·Lukas Janik Jones·Joe Sawada
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Abstract

A universal cycle for a set S of combinatorial objects is a cyclic sequence of length |S| that contains a representative of each element in S exactly once as a substring. Despite the many universal cycle constructions known in the literature for various sets including k-ary strings of length n, permutations of order n, t-subsets of an n-set, and t-multisets of an n-set, remarkably few have efficient decoding (ranking/unranking) algorithms. In this paper we develop the first polynomial time/space decoding algorithms for bounded-weight de Bruijn sequences for strings of length nover an alphabet of size k. The results are then applied to decode universal cycles for t-subsets and t-multisets.

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Daniel Gabric, Wazed Imam, Lukas Janik Jones, Joe Sawada. 2026-03-12. Decoding universal cycles for t-subsets and t-multisets by decoding bounded-weight de Bruijn sequences. https://arxiv.org/abs/2603.11934

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