An inductive approach to constructing Universal Cycles on the k-subsets of [n]

2012/09/30 by Yevgeniy Rudoy · 2 citations
Mathematics · #math.CO

paper · pdf

published as Y. Rudoy, The Electronic Journal of Combinatorics, Volume 20, Issue 2 (2013) 18

arxiv created 2013/04/24 · arxiv updated 2013/04/25

Abstract

In this paper, we introduce a method of constructing Universal Cycles on sets by taking "sums" and "products" of smaller cycles. We demonstrate this new approach by proving that if there exist Universal Cycles on the 4-subsets of [18] and the 4-subsets of [26], then for any integer n which is greater than or equal 18 and equivalent to 2 mod 8, there exists a Universal Cycle on the 4-subsets of [n].

Cited by

• Universal cycle constructions for k-subsets and k-multisets
• Decoding universal cycles for t-subsets and t-multisets by decoding bounded-weight de Bruijn sequences