Hecke insertion and maximal increasing and decreasing sequences in fillings of stack polyominoes
نویسندگان
چکیده
منابع مشابه
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 Jonsson. We also relate our construction to the one recently employed by Christian Krattenthaler,...
متن کاملIncreasing and Decreasing Sequences in Fillings of Moon Polyominoes
We present an adaptation of Jeu de Taquin 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 generali...
متن کاملMaximal increasing sequences in fillings of almost-moon polyominoes
It was proved by Rubey that the number of fillings with zeros and ones of a given moon polyomino that do not contain a northeast chain of size k depends only on the set of columns of the polyomino, but not the shape of the polyomino. Rubey’s proof is an adaption of jeu de taquin and promotion for arbitrary fillings of moon polyominoes. In this paper we present a bijective proof for this result ...
متن کاملIncreasing and Decreasing Sequences of Length Two in 01-fillings of Moon Polyominoes
The main purpose of this paper is to put recent results of Klazar and Noy [10], Kasraoui and Zeng [9], and Chen, Wu and Yan [2], on the enumeration of 2-crossings and 2-nestings in matchings, set partitions and linked partitions in the larger context of enumeration of increasing and decreasing chains in fillings of arrangements of cells. Our work is motivated by the recent paper of Krattenthale...
متن کاملMaximal Fillings of Moon Polyominoes, Simplicial Complexes, and Schubert Polynomials
We exhibit a canonical connection between maximal (0, 1)-fillings of a moon polyomino avoiding north-east chains of a given length and reduced pipe dreams of a certain permutation. Following this approach we show that the simplicial complex of such maximal fillings is a vertex-decomposable, and thus shellable, sphere. In particular, this implies a positivity result for Schubert polynomials. Mor...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2020
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2020.105304