Tiling Generating Functions of Halved Hexagons and Quartered Hexagons

Abstract

We prove exact product formulas for the tiling generating functions of various halved hexagons and quartered hexagons with defects on boundary. Our results generalize the previous work of the first author and the work of Ciucu.

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Notes

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    From now on, we always list the side-lengths of a region in this order.

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Correspondence to Tri Lai.

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This research was supported in part by Simons Foundation Collaboration Grant (# 585923).

Communicated by Matjaz Konvalinka

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Lai, T., Rohatgi, R. Tiling Generating Functions of Halved Hexagons and Quartered Hexagons. Ann. Comb. 25, 471–493 (2021). https://doi.org/10.1007/s00026-021-00537-4

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Keywords

  • Perfect matchings
  • plane partitions
  • lozenge tilings
  • shuffling phenomenon

Mathematics Subject Classification

  • 05A15
  • 05B45