Arvind Ayyer
Correlations in totally symmetric self-complementary plane partitions
Ayyer, Arvind; Chhita, Sunil
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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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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