Correlations in totally symmetric self-complementary plane partitions

Ayyer, Arvind; Chhita, Sunil

doi:10.1112/tlm3.12039

Correlations in totally symmetric self-complementary plane partitions

Ayyer, Arvind; Chhita, Sunil

Authors

Arvind Ayyer

Professor Sunil Chhita sunil.chhita@durham.ac.uk
Professor

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
Publisher	London Mathematical Society
Peer Reviewed	Peer Reviewed
Volume	8
Issue	1
Pages	493-526
DOI	https://doi.org/10.1112/tlm3.12039
Related Public URLs	https://arxiv.org/abs/2012.12623

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

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