Star Transposition Gray Codes for Multiset Permutations
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10450676" target="_blank" >RIV/00216208:11320/22:10450676 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4230/LIPIcs.STACS.2022.34" target="_blank" >https://doi.org/10.4230/LIPIcs.STACS.2022.34</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.STACS.2022.34" target="_blank" >10.4230/LIPIcs.STACS.2022.34</a>
Alternative languages
Result language
angličtina
Original language name
Star Transposition Gray Codes for Multiset Permutations
Original language description
Given integers k >= 2 and a1, . . ., ak >= 1, let a := (a1, . . ., ak) and n := a1 + . . . + ak. An a-multiset permutation is a string of length n that contains exactly ai symbols i for each i = 1, . . ., k. In this work we consider the problem of exhaustively generating all a-multiset permutations by star transpositions, i.e., in each step, the first entry of the string is transposed with any other entry distinct from the first one. This is a far-ranging generalization of several known results. For example, it is known that permutations (a1 = . . . = ak = 1) can be generated by star transpositions, while combinations (k = 2) can be generated by these operations if and only if they are balanced (a1 = a2), with the positive case following from the middle levels theorem. To understand the problem in general, we introduce a parameter Delta(a):= n - 2 max{a1, . . ., ak} that allows us to distinguish three different regimes for this problem. We show that if Delta(a) < 0, then a star transposition Gray code for a-multiset permutations does not exist. We also construct such Gray codes for the case Delta(a) > 0, assuming that they exist for the case INCREMENT (a) = 0. For the case Delta(a) = 0 we present some partial positive results. Our proofs establish Hamilton-connectedness or Hamilton-laceability of the underlying flip graphs, and they answer several cases of a recent conjecture of Shen and Williams. In particular, we prove that the middle levels graph is Hamilton-laceable.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/GA19-08554S" target="_blank" >GA19-08554S: Structures and algorithms in highly symmetric graphs</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Leibniz International Proceedings in Informatics, LIPIcs
ISBN
978-3-95977-222-8
ISSN
1868-8969
e-ISSN
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Number of pages
14
Pages from-to
1-14
Publisher name
Schloss Dagstuhl - Leibniz-Zentrum fur Informatik
Place of publication
Dagstuhl, Germany
Event location
Virtual, Marseille
Event date
May 15, 2022
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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