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.
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