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Gray codes and symmetric chains

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10450675" target="_blank" >RIV/00216208:11320/22:10450675 - isvavai.cz</a>

  • Result on the web

    <a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=z8DP~Q91FK" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=z8DP~Q91FK</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1016/j.jctb.2021.10.008" target="_blank" >10.1016/j.jctb.2021.10.008</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Gray codes and symmetric chains

  • Original language description

    We consider the problem of constructing a cyclic listing of all bitstrings of length 2n + 1 with Hamming weights in the interval [n + 1 - l, n + l], where 1 &lt; l &lt; n + 1, by flipping a single bit in each step. This is a far-ranging generalization of the well-known middle two levels problem (the case l = 1). We provide a solution for the case l = 2, and we solve a relaxed version of the problem for general values of $, by constructing cycle factors for those instances. The proof of the first result uses the lexical matchings introduced by Kierstead and Trotter, which we generalize to arbitrary consecutive levels of the hypercube. The proof of the second result uses symmetric chain decompositions of the hypercube, a concept known from the theory of posets. We also present several new constructions of such decompositions based on lexical matchings. In particular, we construct four pairwise edge disjoint symmetric chain decompositions of the n-dimensional hypercube for any n &gt;= 12. (c) 2021 Elsevier Inc. All rights reserved.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • 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

  • Name of the periodical

    Journal of Combinatorial Theory. Series B

  • ISSN

    0095-8956

  • e-ISSN

    1096-0902

  • Volume of the periodical

    153

  • Issue of the periodical within the volume

    březen

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    30

  • Pages from-to

    31-60

  • UT code for WoS article

    000720434900002

  • EID of the result in the Scopus database

    2-s2.0-85119088131