Ayyer, A and Chhita, S (2021) Correlations in totally symmetric self-complementary plane partitions. In: Transactions of the London Mathematical Society, 8 (1). pp. 493-526.
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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 1/12 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. © 2021 The Authors. Transactions of the London Mathematical Society is copyright © London Mathematical Society.
| Item Type: | Journal Article |
|---|---|
| Publication: | Transactions of the London Mathematical Society |
| Publisher: | John Wiley and Sons Inc |
| Additional Information: | The copyright for this article belongs to Authors |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 20 Jan 2022 06:54 |
| Last Modified: | 20 Jan 2022 06:54 |
| URI: | http://eprints.iisc.ac.in/id/eprint/70996 |
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