NDLI: The spurs of D. H. Lehmer : Hamiltonian paths in neighbor-swap graphs of permutations

Content Provider	Springer Nature Link
Author	Verhoeff, Tom
Copyright Year	2016
Abstract	Consider the graph with all permutations of a symbol sequence as vertices, where two permutations are connected by an edge when they differ by an interchange of two distinct adjacent symbols. In 1965, D. H. Lehmer conjectured that all vertices in this graph can be visited by a Hamiltonian path that is possibly imperfect, in the sense of having spurs. Such a spur visits a vertex twice, with a single vertex in-between. We prove Lehmer’s conjecture for binary permutations that involve only two distinct symbols. For general symbol sequences, we identify the stutter permutations as candidate spur tips, and prove that the non-stutter permutations admit a disjoint cycle cover. We also provide new (simpler) proofs for some known results.
Ending Page	310
Page Count	16
Starting Page	295
File Format	PDF
ISSN	09251022
e-ISSN	15737586
Journal	Designs, Codes and Cryptography
Issue Number	1-2
Volume Number	84
Language	English
Publisher	Springer US
Publisher Date	2016-11-14
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Minimal-change generation Information and Communication, Circuits Data Structures, Cryptology and Information Theory Permutation Discrete Mathematics in Computer Science Data Encryption Hamiltonian path Coding and Information Theory Eulerian and Hamiltonian graphs Combinatorics Paths and cycles
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Discrete Mathematics and Combinatorics Theoretical Computer Science Computer Science Applications

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