Related papers: Relative Combinatorial Asphericity
Assortativity measures the tendency of a vertex in a network being connected by other vertexes with respect to some vertex-specific features. Classical assortativity coefficients are defined for unweighted and undirected networks with…
We prove a combination theorem for trees of (strongly) relatively hyperbolic spaces and finite graphs of (strongly) relatively hyperbolic groups. This gives a geometric extension of Bestvina and Feighn's Combination Theorem for hyperbolic…
The material gives a new combinatorial proof of the multiplicative property of the S-transform. In particular, several properties of the coefficients of its inverse are connected to non-crossing linked partitions and planar trees.
We study three different kinds of embeddings of tree patterns: weakly-injective, ancestor-preserving, and lca-preserving. While each of them is often referred to as injective embedding, they form a proper hierarchy and their computational…
We discuss the use of methods coming from integrable systems to study problems of enumerative and algebraic combinatorics, and develop two examples: the enumeration of Alternating Sign Matrices and related combinatorial objects, and the…
This is a survey on recent developments on unimodality, log-concavity and real-rootedness in combinatorics. Stanley and Brenti have written extensive surveys of various techniques that can be used to prove real-rootedness, log-concavity or…
A 2-complex $K$ has collapsing non-positive immersion if for every combinatorial immersion $X\to K$, where $X$ is finite, connected and does not allow collapses, either $\chi(X)\le 0$ or $X$ is point. This concept is due to Wise who also…
This continues the investigation of a combinatorial model for the variation of dynamics in the family of rational maps of degree two, by concentrating on those varieties in which one critical point is periodic. We prove some general results…
In this article we tackle the combinatorics of coloured hard-dimer objects. This is achieved by identifying coloured hard-dimer configurations with a certain class of rooted trees that allow for an algebraic treatment in terms of…
This paper proves that two differently defined rooted binary trees are isomorphic. The first tree is one associated to a version of Farey sequences where the vertices correspond to the open intervals formed by two successive terms in the…
The class of self-nested trees presents remarkable compression properties because of the systematic repetition of subtrees in their structure. In this paper, we provide a better combinatorial characterization of this specific family of…
We establish a new simple explicit description of combinatorial wall-crossing for the rational Cherednik algebra applied to the trivial representation. In this way we recover a theorem of P. Dimakis and G. Yue. We also present two…
We define combinatorial Floer homology of a transverse pair of noncontractibe nonisotopic embedded loops in an oriented 2-manifold without boundary, prove that it is invariant under isotopy, and prove that it is isomorphic to the original…
We introduce combinatorial objects named matricubes that provide a generalization of the theory of matroids. As matroids provide a combinatorial axiomatization of hyperplane arrangements, matricubes provide a combinatorial axiomatization of…
To allow for a comparison of theoretical predictions for spin chains with experimental data, it is often important to take impurity effects as well as interchain couplings into account. Here we present the field theory for finite spin…
When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in…
The distance of a binary operation from being associative can be "measured" by its associative spectrum, an appropriate sequence of positive integers. Particular instances and general properties of associative spectra are studied.
A hyperplane arrangement is called formal provided all linear dependencies among the defining forms of the hyperplanes are generated by ones corresponding to intersections of codimension two. The significance of this notion stems from the…
Treewidth is a well-known graph invariant with multiple interesting applications in combinatorics. On the practical side, many NP-complete problems are polynomial-time (sometimes even linear-time) solvable on graphs of bounded treewidth. On…
This paper proposes an algebraic view of trees which opens the doors to an alternative computational scheme with respect to classic algorithms. In particular, it is shown that this view is very well-suited for machine learning and…