Title
On Universal Cycles for New Classes of Combinatorial Structures
Document Type
Article
Publication Date
12-1-2011
Description
A universal cycle (u-cycle) is a compact listing of a collection of combinatorial objects. In this paper, we use natural encodings of these objects to show the existence of u-cycles for collections of subsets, restricted multisets, and lattice paths. For subsets, we show that a u-cycle exists for the κ-subsets of an n-set if we let κ vary in a non zero length interval. We use this result to construct a "covering" of length (1+o(1))(n/κ) for all subsets of [n] of size exactly κ with a specific formula for the o(1) term. We also show that u-cycles exist for all n-length words over some alphabet ∑, which contain all characters from R ⊂ ∑. Using this result we provide u-cycles for encodings of Sperner families of size 2 and proper chains of subsets.
Citation Information
Blanca, Antonio; and Godbole, Anant P.. 2011. On Universal Cycles for New Classes of Combinatorial Structures. SIAM Journal on Discrete Mathematics. Vol.25(4). 1832-1842. https://doi.org/10.1137/100805674 ISSN: 0895-4801