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Correlations in totally symmetric self-complementary plane partitions

Ayyer, Arvind; Chhita, Sunil

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Authors

Arvind Ayyer



Abstract

Totally symmetric self-complementary plane partitions (TSSCPPs) are boxed plane partitions with the maximum possible symmetry. We use the well-known representation of TSSCPPs as a dimer model on a honeycomb graph enclosed in one-twelfth of a hexagon with free boundary to express them as perfect matchings of a family of non-bipartite planar graphs. Our main result is that the edges of the TSSCPPs form a Pfaffian point process, for which we give explicit formulas for the inverse Kasteleyn matrix. Preliminary analysis of these correlations are then used to give a precise conjecture for the limit shape of TSSCPPs in the scaling limit.

Citation

Ayyer, A., & Chhita, S. (2021). Correlations in totally symmetric self-complementary plane partitions. Transactions of the London Mathematical Society, 8(1), 493-526. https://doi.org/10.1112/tlm3.12039

Journal Article Type Article
Acceptance Date Aug 28, 2021
Online Publication Date Oct 28, 2021
Publication Date 2021-12
Deposit Date Sep 11, 2021
Publicly Available Date Nov 25, 2021
Journal Transactions of the London Mathematical Society
Electronic ISSN 2052-4986
Publisher London Mathematical Society
Peer Reviewed Peer Reviewed
Volume 8
Issue 1
Pages 493-526
DOI https://doi.org/10.1112/tlm3.12039
Public URL https://durham-repository.worktribe.com/output/1240952
Related Public URLs https://arxiv.org/abs/2012.12623

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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright Statement
© 2021 The Authors. Transactions of the London Mathematical Society is copyright © London Mathematical Society.

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.





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