English

A Shuffling Theorem for Reflectively Symmetric Tilings

Combinatorics 2019-07-09 v2

Abstract

In arXiv:1905.08311, the author and Rohatgi proved a shuffling theorem for doubly-dented hexagons. In particular, we showed that shuffling removed unit triangles along a horizontal axis in a hexagon only changes the tiling number by a simple multiplicative factor. In this paper, we consider a similar phenomenon for a symmetry class of tilings, the reflectively symmetric tilings, of the doubly-dented hexagons. We also prove several shuffling theorems for halved hexagons. These theorems generalize a number of known results in the enumeration of halved hexagons.

Keywords

Cite

@article{arxiv.1905.09268,
  title  = {A Shuffling Theorem for Reflectively Symmetric Tilings},
  author = {Tri Lai},
  journal= {arXiv preprint arXiv:1905.09268},
  year   = {2019}
}

Comments

Second version: 21 pages

R2 v1 2026-06-23T09:18:08.178Z