Avoiding Monotone Chains in Fillings of Layer Polyominoes

作者：Phillipson Mitch^*; Yan Catherine H

来源：Annals of Combinatorics, 2016, 20(4): 883-897.

DOI：10.1007/s00026-016-0326-9

• polyomino
• noncrossing
• nonnesting
• fillings

In this paper we give simple bijective proofs that the number of fillings of layer polyominoes with no northeast chains is the same as the number with no southeast chains. We consider 01-fillings and -fillings and prove the results for both strong chains where the smallest rectangle containing the chain is also in the polyomino, and for regular chains where only the corners of the smallest rectangle containing the chain are required to be in the polyomino.

• 出版日期2016-12