Increasing and decreasing sequences in fillings of moon polyominoes

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...

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Bibliographic Details
Published in:Advances in applied mathematics 2011-07, Vol.47 (1), p.57-87
Main Author: Rubey, Martin
Format: Article
Language:English
Subjects:
Adaptation
Construction
Crossings and nestings
Evacuation
Exact sciences and technology
General mathematics
General, history and biography
Growth diagrams
Jeu de taquin
L-convex polyominoes
Mathematical analysis
Mathematics
Moon
Moon polyominoes
Numerical analysis
Numerical analysis. Scientific computation
Plactic monoid
Promotion
Sciences and techniques of general use
Symmetry
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Summary: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.
ISSN:0196-8858
1090-2074
DOI:10.1016/j.aam.2009.11.013