On universal cycles for new classes of combinatorial structures

Antonio Blanca, Anant P. Godbole

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)1832-1842
Number of pages11
JournalSIAM Journal on Discrete Mathematics
Volume25
Issue number4
DOIs
Publication statusPublished - Dec 1 2011

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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