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Maximal fillings of moon polyominoes, simplicial complexes, and Schubert polynomials
filling of moon polyomino k-triangulation fan of Dyck paths
2010/12/10
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.
Maximal 0-1 fillings of moon polyominoes with restricted chain-lengths and rc-graphs
multitriangulations rc-graphs Edelman-Greene insertion Schubert polynomials
2010/12/9
We show that maximal 0-1-fillings of moon polynomials,with restricted chain lengths, can be identified with certain rc-graphs, also known as pipe dreams. In particular, this exhibits
a connection bet...
On Some fundamental aspects of Polyominoes on Random Voronoi Tilings
fundamental aspects Polyominoes Random Voronoi Tilings
2010/12/9
Consider a Voronoi tiling of Rd based on a realization of a inhomogeneous Poisson random set. A Voronoi polyomino is a finite and connected union of Voronoi tiles.In this paper we provide tail bounds ...
3D Polyominoes inscribed in a rectangular prism
polycube inscribed polyomino enumeration rectangular prism generating function
2010/12/13
We introduce a family of 3D combinatorial objects that we define as minimal 3D polyominoes
inscribed in a rectanglar prism. These objects are connected sets of unitary cubic cells inscribed in a give...
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...
Mixed Statistics on 01-Fillings of Moon Polyominoes
mixed statistic polyomino symmetric distribution
2014/6/3
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 ...
