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Correlations in totally symmetric self-complementary plane partitions

Ayyer, Arvind and Chhita, Sunil (2021) 'Correlations in totally symmetric self-complementary plane partitions.', Transactions of the London Mathematical Society, 8 (1). pp. 493-526.


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.

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Publisher 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.
Date accepted:28 August 2021
Date deposited:14 September 2021
Date of first online publication:28 October 2021
Date first made open access:25 November 2021

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