Svetlana Poznanović ; Catherine H. Yan - Maximal increasing sequences in fillings of almost-moon polyominoes

dmtcs:2477 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) - https://doi.org/10.46298/dmtcs.2477
Maximal increasing sequences in fillings of almost-moon polyominoesArticle

Authors: Svetlana Poznanović 1; Catherine H. Yan ORCID2

  • 1 Department of Mathematical Sciences [Clemson]
  • 2 Department of Mathematics [Texas A&M University]

It was proved by Rubey that the number of fillings with zeros and ones of a given moon polyomino thatdo not contain a northeast chain of a fixed size depends only on the set of column lengths of the polyomino. Rubey’sproof uses an adaption of jeu de taquin and promotion for arbitrary fillings of moon polyominoes and deduces theresult for 01-fillings via a variation of the pigeonhole principle. In this paper we present the first completely bijectiveproof of this result by considering fillings of almost-moon polyominoes, which are moon polyominoes after removingone of the rows. More precisely, we construct a simple bijection which preserves the size of the largest northeast chainof the fillings when two adjacent rows of the polyomino are exchanged. This bijection also preserves the column sumof the fillings. In addition, we also present a simple bijection that preserves the size of the largest northeast chains, therow sum and the column sum if every row of the filling has at most one 1. Thereby, we not only provide a bijectiveproof of Rubey’s result but also two refinements of it.


Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Imported on: November 21, 2016
Keywords: moon polyominoes,maximal chains,01-fillings,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • Problems in Enumerative Combinatorics and Applications; Funder: National Science Foundation; Code: 1161414
  • Analysis of stochastic context-free grammars for RNA secondary structure prediction; Funder: National Science Foundation; Code: 1312817

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