Maximal 0–1-fillings of moon polyominoes with restricted chain lengths and rc-graphs
نویسندگان
چکیده
منابع مشابه
Maximal 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...
متن کاملMixed Statistics on 01-Fillings of Moon Polyominoes
We establish a stronger symmetry between the numbers of northeast and southeast chains in the context of 01-fillings of moon polyominoes. Let M be a moon polyomino with n rows and m columns. Consider all the 01-fillings of M in which every row has at most one 1. We introduce four mixed statistics with respect to a bipartition of rows or columns of M. More precisely, let S ⊆ {1, 2, . . . , n} an...
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 کاملMajor index for 01-fillings of moon polyominoes
We propose a major index statistic on 01-fillings of moon polyominoes which, when specialized to certain shapes, reduces to the major index for permutations and set partitions. We consider the set F(M, s;A) of all 01-fillings of a moon polyomino M with given column sum s whose empty rows are A, and prove that this major index has the same distribution as the number of north-east chains, which a...
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...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2012
ISSN: 0196-8858
DOI: 10.1016/j.aam.2011.05.005