Permutation Totally Symmetric Self-Complementary Plane Partitions

Permutation Totally Symmetric Self-Complementary Plane Partitions c Springer Basel AG 2018 Annals of Combinatorics 22 (2018) 1-••• Ann. Comb. 12 (2009) 479–492 Annals of Combinatorics 0218-0006/18/010001-10 https://doi.org/10.1007/s00026-018-0394-0 Annals of Combinatorics DOI *********** © Springer International Publishing AG, part of Springer Nature 2018 Permutation Totally Symmetric Self-Complementary Plane Partitions Jessica Striker Department of Mathematics, North Dakota State University, Fargo, ND 58108-6050, USA jessica.striker@ndsu.edu Received September 18, 2015 Mathematics Subject Classification: 05A05, 06A07 Abstract. Alternating sign matrices and totally symmetric self-complementary plane parti- tions are equinumerous sets of objects for which no explicit bijection is known. In this paper, we identify a subset of totally symmetric self-complementary plane partitions corresponding to permutations by giving a statistic-preserving bijection to permutation matrices, which are a subset of alternating sign matrices. We use this bijection to define a new partial order on permu- tations, and prove this new poset contains both the Tamari lattice and the Catalan distributive lattice as subposets. We also study a new partial order on totally symmetric self-complementary plane partitions arising from this perspective and show that this is a distributive lattice related to Bruhat order when restricted to permutations. Keywords: alternating sign matrix, permutation, plane partition, poset, Tamari lattice 1. Introduction Alternating sign matrices (ASM) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Combinatorics Springer Journals

Permutation Totally Symmetric Self-Complementary Plane Partitions

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Publisher
Springer International Publishing
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Combinatorics
ISSN
0218-0006
eISSN
0219-3094
D.O.I.
10.1007/s00026-018-0394-0
Publisher site
See Article on Publisher Site

Abstract

c Springer Basel AG 2018 Annals of Combinatorics 22 (2018) 1-••• Ann. Comb. 12 (2009) 479–492 Annals of Combinatorics 0218-0006/18/010001-10 https://doi.org/10.1007/s00026-018-0394-0 Annals of Combinatorics DOI *********** © Springer International Publishing AG, part of Springer Nature 2018 Permutation Totally Symmetric Self-Complementary Plane Partitions Jessica Striker Department of Mathematics, North Dakota State University, Fargo, ND 58108-6050, USA jessica.striker@ndsu.edu Received September 18, 2015 Mathematics Subject Classification: 05A05, 06A07 Abstract. Alternating sign matrices and totally symmetric self-complementary plane parti- tions are equinumerous sets of objects for which no explicit bijection is known. In this paper, we identify a subset of totally symmetric self-complementary plane partitions corresponding to permutations by giving a statistic-preserving bijection to permutation matrices, which are a subset of alternating sign matrices. We use this bijection to define a new partial order on permu- tations, and prove this new poset contains both the Tamari lattice and the Catalan distributive lattice as subposets. We also study a new partial order on totally symmetric self-complementary plane partitions arising from this perspective and show that this is a distributive lattice related to Bruhat order when restricted to permutations. Keywords: alternating sign matrix, permutation, plane partition, poset, Tamari lattice 1. Introduction Alternating sign matrices (ASM)

Journal

Annals of CombinatoricsSpringer Journals

Published: Jun 6, 2018

References

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