Decoding universal cycles for t-subsets and t-multisets by decoding bounded-weight de Bruijn sequences
Discrete Mathematics
2026-03-13 v1 Information Theory
Combinatorics
math.IT
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.
Keywords
Cite
@article{arxiv.2603.11934,
title = {Decoding universal cycles for t-subsets and t-multisets by decoding bounded-weight de Bruijn sequences},
author = {Daniel Gabric and Wazed Imam and Lukas Janik Jones and Joe Sawada},
journal= {arXiv preprint arXiv:2603.11934},
year = {2026}
}