Near|Universal Cycles for Subsets Exist

[0809.3725] Near universal cycles for subsets exist - arXiv

We say that S is a {\it universal cycle} ((n,k)-Ucycle) for k-subsets of [n] if every such subset appears exactly once contiguously in S, and is ...

Near-Universal Cycles for Subsets Exist | SIAM Journal on Discrete ...

We say that S is a universal cycle ( ( n , k ) -Ucycle) for k-subsets of [ n ] if every such subset appears exactly once contiguously in S, and is a Ucycle ...

Near-Universal Cycles for Subsets Exist

Abstract. Let S be a cyclic n-ary sequence. We say that S is a universal cycle. ((n, k)-Ucycle) for k-subsets of [n] if every such subset ...

(PDF) Near-Universal Cycles for Subsets Exist - ResearchGate

PDF | Let S be a cyclic n-ary sequence. We say that S is a {\it universal cycle} ((n,k)-Ucycle) for k-subsets of [n] if every such subset appears.

Near-Universal Cycles for Subsets Exist - ACM Digital Library

Let $S$ be a cyclic $n$-ary sequence. We say that $S$ is a universal cycle ($(n,k)$-Ucycle) for $k$-subsets of $[n]$ if every such subset appears exactly ...

Universal cycles for $k$-sets of an $n$-set - MathOverflow

Conjecture. For every natural k there is n0(k) such that a universal cycle for S(n,k) always exists provided that k divides (n−1k−1) and n≥n0(k) ...

On Universal Cycles for k-Subsets of an n-Set

A universal cycle, or Ucycle, for k-subsets of $[ n ] = \{ 1, \ldots,n \}$ is a cyclic sequence of $\begin{pmatrix} n \\ k \end{pmatrix}$ integers with the ...

Universal and Near-Universal Cycles of Set Partitions

Near-universal cycles for subsets exist. SIAM J. Discrete Math., 23, 1441–1449, 2009. the electronic journal of combinatorics 22 (2015), #P00. 14. Page 15. [4] ...

Universal cycles of k-subsets and k-permutations - ScienceDirect.com

No universal cycle of the 4-combinations with repetition of (0, 1, . , n- l} can exist unless (n, 4)= 1 or n=6(mod 8); this leads to Theorem 2.7. In a similar ...

On universal cycles for new classes of combinatorial structures ...

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.

De Bruijn Sequence and Universal Cycle Constructions

Universal cycles for the k k -subsets of {1,2,…,n} { 1 , 2 , … , n } have been generally studied by considering a standard string representation, i.e., either ...

Universal and Near-Universal Cycles of Set Partitions - NASA/ADS

We also show that there exist universal cycles of partitions of $[n]$ into $k$ subsets of distinct sizes when $k$ is sufficiently smaller than $n$, and ...

Euler tours in hypergraphs - School of Mathematics

Moyer, Near-universal cycles for subsets exist, SIAM J. Discrete Math. 23 (2009), 1441 1449. [8] M. D ebski and Z. Lonc, Universal cycle ...

Graph universal cycles of combinatorial objects - ScienceDirect.com

This leads to Theorem 2.5, namely the existence of Gucycles for k-subsets of an n-set, for all values of k , n . •. A class of multiple edge subgraphs of ...

Universal Cycle Packings and Coverings for k-Subsets of an n-Set

1.2 Near-Universal Cycles ... Formally, by an (n, k)-Ucycle packing (resp. (n, k)-Ucycle covering) we mean a sequence (a_0,a_1,\ldots , a_{m-1}) ...

Universal cycles of k-subsets and k-permutations - Semantic Scholar

Universal cycles of k-subsets and k-permutations · B. Jackson · Published in Discrete Mathematics 1 July 1993 · Mathematics.

On Universal Cycles for k-Subsets of an n-Set - ACM Digital Library

A universal cycle, or Ucycle, for k-subsets of [n] = {1,...,n} is a cyclic sequence of $(\stackerel{n}{k})$ integers with the property that each subset of

An inductive approach to constructing universal cycles on the k ...

We demonstrate this new approach by proving that if there exist universal cycles ... exists a universal cycle on the 4-subsets of [n]. Introduction. Consider the ...

Graph universal cycles of combinatorial objects - NSF PAR

This leads to Theorem 2.5, namely the existence of Gucycles for k-subsets of an n-set, for all values of k,n. Page 5. A. Cantwell et al. / Advances in Applied ...

Products of Universal Cycles - UCSD

These only exist for certain k and n; here even the existence is an open research problem. This is a universal cycle for k-subsets of an n-set. See Jackson [11] ...