Increasing and Decreasing Sequences in Fillings of Moon Polyominoes

Details Increasing and Decreasing Sequences in Fillings of Moon Polyominoes Increasing and Decreasing Sequences in Fillings of Moon Polyominoes

2006-04-06

arxiv.org/abs/math/0604140v5

Mathematics

Combinatorics

fixed typos

Scientific paper

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.

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