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Combinatorial generation via permutation languages. II. Lattice congruences

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Hoang, Hung P. and Mutze, Torsten (2021) Combinatorial generation via permutation languages. II. Lattice congruences. Israel Journal of Mathematics, 244 . pp. 359-417. doi:10.1007/s11856-021-2186-1

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Official URL: https://doi.org/10.1007/s11856-021-2186-1

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Abstract

This paper deals with lattice congruences of the weak order on the symmetric group, and initiates the investigation of the cover graphs of the corresponding lattice quotients. These graphs also arise as the skeleta of the so-called quotientopes, a family of polytopes recently introduced by Pilaud and Santos [Bull. Lond. Math. Soc., 51:406–420, 2019], which generalize permutahedra, associahedra, hypercubes and several other polytopes. We prove that all of these graphs have a Hamilton path, which can be computed by a simple greedy algorithm. This is an application of our framework for exhaustively generating various classes of combinatorial objects by encoding them as permutations. We also characterize which of these graphs are vertex-transitive or regular via their arc diagrams, give corresponding precise and asymptotic counting results, and we determine their minimum and maximum degrees.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions: Faculty of Science, Engineering and Medicine > Science > Computer Science
Library of Congress Subject Headings (LCSH): Congruence lattices , Symmetry groups , Computer science -- Mathematics, Polytopes , Permutations
Journal or Publication Title: Israel Journal of Mathematics
Publisher: Springer
ISSN: 0021-2172
Official Date: September 2021
Dates:
DateEvent
September 2021Published
21 August 2021Available
20 July 2020Accepted
Volume: 244
Page Range: pp. 359-417
DOI: 10.1007/s11856-021-2186-1
Status: Peer Reviewed
Publication Status: Published
Reuse Statement (publisher, data, author rights): This is a post-peer-review, pre-copyedit version of an article published in Israel Journal of Mathematics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11856-021-2186-1
Access rights to Published version: Restricted or Subscription Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
GA 19-08554SGrantová Agentura České Republikyhttp://dx.doi.org/10.13039/501100001824
413902284[DFG] Deutsche Forschungsgemeinschafthttp://dx.doi.org/10.13039/501100001659
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