Increasing and Decreasing Sequences in Fillings of Moon Polyominoes

2006/04/06 by Martin Rubey, Rubey, Martin · 1 citation
Mathematics · #05A15 (Primary) #05A17 05A19 05E10 (Secondary) #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.CO #msc:05A15 #msc:05A17 #msc:05A19 #msc:05E10

paper · pdf · doi:10.48550/arxiv.math/0604140

fixed typos

openalex publication_date 2006/04/06 · arxiv created 2009/11/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present an adaptation of jeu de taquin and promotion for arbitrary fillings of moon polyominoes. Using this construction we show various symmetry properties of such fillings taking into account the lengths of longest increasing and decreasing chains. In particular, we prove a conjecture of Jakob Jonsson. We also relate our construction to the one recently employed by Christian Krattenthaler, thus generalising his results.

Cited by

• Maximal fillings of moon polyominoes, simplicial complexes, and Schubert polynomials

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