Related papers: On permutations avoiding partially ordered pattern…
Topological drawings are natural representations of graphs in the plane, where vertices are represented by points, and edges by curves connecting the points. Topological drawings of complete graphs and of complete bipartite graphs have been…
The primary goal of this paper is to abstract notions, results and constructions from the theory of categories to the broader setting of plots. Loosely speaking, a plot can be thought of as a non-associative non-unital category with a…
The landscape of applications and subroutines relying on shortest path computations continues to grow steadily. This growth is driven by the undeniable success of shortest path algorithms in theory and practice. It also introduces new…
We consider the family of guarded and unguarded ordered logics, that constitute a recently rediscovered family of decidable fragments of first-order logic (FO), in which the order of quantification of variables coincides with the order in…
A simple undirected graph is said to be {\em semisymmetric} if it is regular and edge-transitive but not vertex-transitive. Every semisymmetric graph is a bipartite graph with two parts of equal size. It was proved in [{\em J. Combin.…
Word-representable graphs, which are the same as semi-transitively orientable graphs, generalize several fundamental classes of graphs. In this paper we propose a novel approach to study word-representability of graphs using a technique of…
We introduce an algorithm that conjectures the structure of a permutation class in the form of a disjoint cover of "rules"; similar to generalized grid classes. The cover is usually easily verified by a human and translated into an…
We classify all bi-vincular patterns of length two and three according to the number of permutations avoiding them. These patterns were recently defined by Bousquet-Melou et. al., and are natural generalizations of Babson and…
In the last years, different types of patterns in permutations have been studied: vincular, bivincular and mesh patterns, just to name a few. Every type of permutation pattern naturally defines a corresponding computational problem: Given a…
We compare a traditional and non-traditional view on the subject of P-partitions, leading to formulas counting linear extensions of certain posets.
The exchange graph of a cluster algebra encodes the combinatorics of mutations of clusters. Through the recent "categorifications" of cluster algebras using representation theory one obtains a whole variety of exchange graphs associated…
Extending the notion of pattern avoidance in permutations, we study matchings and set partitions whose arc diagram representation avoids a given configuration of three arcs. These configurations, which generalize 3-crossings and 3-nestings,…
We describe the modular operad structure on the moduli spaces of pointed stable curves equipped with an admissible $G$-cover. To do this we are forced to introduce the notion of an operad colored not by a set but by the objects of a…
We consider bipartite graphs definable in o-minimal structures, in which the edge relation $G$ is a finite union of graphs of certain measure-preserving maps. We establish a fact on the existence of definable matchings with few short…
We introduce the bicategory of bialgebras with coverings (which can be thought of as coalgebra-indexed families of morphisms), and provide a motivating application to the transfer of formulas for primitives and antipode. Additionally, we…
Bilinear maps and their classifying tensor products are well-known in the theory of linear algebra, and their generalization to algebras of commutative monads is a classical result of monad theory. Motivated by constructions needed in…
A partial order $\prec$ on $[n]$ is naturally labelled (NL) if $x\prec y$ implies $x<y$. We establish a bijection between {3, 2+2}-free NL posets and 12-34-avoiding permutations, determine functional equations satisfied by their generating…
We generalize the construction of affine polar graphs in two different ways to obtain new partial difference sets and amorphic association schemes. The first generalization uses a combination of quadratic forms and uniform cyclotomy. In the…
A half-square of a bipartite graph $B=(X,Y,E_B)$ has one color class of $B$ as vertex set, say $X$; two vertices are adjacent whenever they have a common neighbor in $Y$. If $G=(V,E_G)$ is the half-square of a planar bipartite graph…
A bipartite graph G is known to be Pfaffian if and only if it does not contain an even subdivision H of $K_{3,3}$ such that $G - VH$ contains a 1-factor. However a general characterisation of Pfaffian graphs in terms of forbidden subgraphs…