Graph Universal Cycles of Permutations and Set Partitions

Universal cycles are cyclic strings of elements which encode various combinatorial objects, such as permutations, in different "windows" along the code.

Graph universal cycles of combinatorial objects - ScienceDirect.com

Permutations are represented via their permutation graphs, and set partitions through disjoint unions of complete graphs. Introduction. A somewhat loose ...

Graph universal cycles: Compression and connections to universal ...

Universal cycles for other families of combinatorial objects—such as sets, permutations, and set partitions—were studied in [8]. In contrast to De Bruijn cycles ...

Graph Universal Cycles of Combinatorial Objects

... ” edges in C5. Permutations are represented via their permutation graphs, and set partitions through disjoint unions of complete graphs.

On Universal Cycles of Labeled Graphs - Greg Brockman

cycles). The concept easily lends itself to extension, and universal cycles for permutations, partitions, and certain classes of functions are well-studied ...

Universal and Near-Universal Cycles of Set Partitions

The graph G5,3 is shown again in Figure 3 with edges labeled with their associated permutations (expressed in cycle notation with fixed points supressed).

Graph universal cycles of combinatorial objects - NSF PAR

Universal cycles for combinatorial structures - UCSD Math

of de Bruijn cycles for a variety of families of combinatorial structures, including permutations, partitions and subsets of a finite set. 1. Introduction.

Compression and Connections to Universal Cycles - arXiv

... graph universal cycles for sets, multisets, permutations, permutation involutions, and set partitions by encoding them as graphs. In Section ...

On a Greedy Algorithm to Construct Universal Cycles for Permutations

graph and then dealing with partially ordered sets. In this paper, we offer ... An explicit universal cycle for the (n − 1)- permutations of an n-set.

Graph Universal Cycles of Combinatorial Objects - ResearchGate

Permutations are represented via their permutation graphs, and set partitions through disjoint unions of complete graphs.

Universal Cycles

other combinatorial structures such as permutations and partitions of a set. ... Figure 8: Eulerian graph for partitions of a set with 3 elements. Next, we ...

Shortened Universal Cycles for Permutations - Bernard Lidický

... universal cycles for other combinatorial objects such as permutations, sets, and set partitions. A universal word for F is the non-cyclic ...

Universal Cycles for Permutations - arXiv

them include F being the set of permutations of an n-set, r-subsets of an n-set, and partitions of an n-set. ... Figure 1: The cycles C ...

Explicit Constructions of Universal Cycles on Partial Permutations

Suppose there is a set of transitions (or functions) defined on Sn, then we can draw a directed graph with all the permutations as vertices and all the ...

Universal and Near-Universal Cycles of Set Partitions - ResearchGate

... permutation product is the identity. 15. Page 16. Figure 3: G5,3 with associated permutations. Proof. Fix a representation r of the vertex at ...

[PDF] Universal and Near-Universal Cycles of Set Partitions

Graph universal cycles of combinatorial objects · Amelia CantwellJuliann ... cycles for words and permutations. Expand. 1 Citation · PDF. Add to Library.

Shortened Universal Cycles for Permutations - NSF PAR

... universal cycles for other combinatorial objects such as permutations, sets, and set partitions. A universal word for F is the non-cyclic ...

Universal cycles for weak orders

In this case the set A is the set of all permutations of an n-set, which has been a well-known and difficult ucycle problem [12, 15]. Proof. Construct a graph ...

On a family of universal cycles for multi-dimensional permutations

It was shown in [2] that u-cycles for set partitions exist for any n ≥ 4. ... The graph theoretic approach to construct u-cycles for permutations. The ...