On orthogonal symmetric chain decompositions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10400341" target="_blank" >RIV/00216208:11320/19:10400341 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=pNNBfKX8Cx" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=pNNBfKX8Cx</a>
DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
On orthogonal symmetric chain decompositions
Original language description
The n-cube is the poset obtained by ordering all subsets of {1, ..., n} by inclusion, and it can be partitioned into ((n)(left perpendicular n/2 right perpendicular)) chains, which is the minimum possible number. Two such decompositions of the n-cube are called orthogonal if any two chains of the decompositions share at most a single element. Shearer and Kleit-man conjectured in 1979 that the n-cube has left perpendicular n/2 right perpendicular+ 1 pairwise orthogonal decompositions into the minimum number of chains, and they constructed two such decompositions. Spink recently improved this by showing that the n-cube has three pairwise orthogonal chain decompositions for n >= 24. In this paper, we construct four pairwise orthogonal chain decompositions of the n-cube for n >= 60. We also construct five pairwise edge-disjoint symmetric chain decompositions of the n-cube for n >= 90, where edge-disjointness is a slightly weaker notion than orthogonality, improving on a recent result by Gregor, Jager, Mutze, Sawada, and Wille.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
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
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Electronic Journal of Combinatorics
ISSN
1077-8926
e-ISSN
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Volume of the periodical
26
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
32
Pages from-to
P3.64
UT code for WoS article
000488213000010
EID of the result in the Scopus database
2-s2.0-85073629489