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...

A polyomino is said to be L-convex if any two of its cells are connected by a 4-connected inner path that changes direction at most once. The 2-dimensional language representing such polyominoes has been recently proved to be recognizable by tiling systems by S. Brocchi, A. Frosini, R. Pinzani and S. Rinaldi. In an attempt to compare recognition power of tiling systems and cellular automata, we...

Boltzmann samplers and the recursive method are prominent algorithmic frameworks for the approximate-size and exact-size random generation of large combinatorial structures, such as maps, tilings, RNA sequences or various tree-like structures. In their multiparametric variants, these samplers allow to control the profile of expected values corresponding to multiple combinatorial parameters. One...

A toric quantum error-correcting code construction procedure is presented in this work. new class of an infinite family codes provided by constructing a classical cyclic on the square lattice $${\mathbb {Z}}_{q}\times {\mathbb {Z}}_{q}$$ for all odd integers $$q\ge 5$$ and, consequently, are constructed such lattices and from geometrically uniform regardless whether q can be represented as sum ...

Abstract In micro- and nano-scale systems, particles can be moved by using an external force like gravity or a magnetic field. the presence of adhesive that attach to each other, challenge is decide whether shape constructible. Previous work provides class shapes for which constructibility decided efficiently when move maximally into same direction induced global signal. this paper we consider ...

We give a polyomino characterisation of recurrent configurations of the sandpile model on the complete bipartite graph Km,n in which one designated vertex is the sink. We present a bijection from these recurrent configurations to decorated parallelogram polyominoes whose bounding box is a m× n rectangle. Other combinatorial structures appear in special cases of this correspondence: for example ...

We are interested in description of set of pictures by string languages by using several semantics segments segments with blank moves and pixels We give a method to code the Post correspondence problem in rational picture languages in order to show the undecidability of existence of words satisfying a given property in a rational language Introduction In order to use the well known tools of the...