Related papers: Extending the symbolic method in enumerative combi…
We apply model theoretic methods to the problem of existence of countable universal graphs with finitely many forbidden connected subgraphs. We show that to a large extent the question reduces to one of local finiteness of an…
Analytic combinatorics studies asymptotic properties of families of combinatorial objects using complex analysis on their generating functions. In their reference book on the subject, Flajolet and Sedgewick describe a general approach that…
We introduce the notion of universal graphs as a tool for constructing algorithms solving games of infinite duration such as parity games and mean payoff games. In the first part we develop the theory of universal graphs, with two goals:…
Graph-based semantic representations are valuable in natural language processing, where it is often simple and effective to represent linguistic concepts as nodes, and relations as edges between them. Several attempts has been made to find…
We study semantic models of probabilistic programming languages over graphs, and establish a connection to graphons from graph theory and combinatorics. We show that every well-behaved equational theory for our graph probabilistic…
We initiate the study of what we refer to as random walk labelings of graphs. These are graph labelings that are obtainable by performing a random walk on the graph, such that the labeling occurs increasingly whenever an unlabeled vertex is…
We show that the essentially algebraic theory of generalized algebraic theories, regarded as a category with finite limits, has a universal exponentiable arrow in the sense that any exponentiable arrow in any category with finite limits is…
We consider a Random Graph Model on $\mathbb{Z}^{d}$ that incorporates the interplay between the statistics of the graph and the underlying space where the vertices are located. Based on a graphical construction of the model as the…
We study models of weighted exponential random graphs in the large network limit. These models have recently been proposed to model weighted network data arising from a host of applications including socio-econometric data such as migration…
We prove Bowen's conjecture that every sequence of finite graphs that locally converges to the Cayley graph of a countably infinite group with Kazhdan Property (T) is essentially a vertex-disjoint union of expander graphs. We characterize…
Motivated by limits of critical inhomogeneous random graphs, we construct a family of sequences of measured metric spaces that we call continuous multiplicative graphs, that are expected to be the universal limit of graphs related to the…
Several approaches have been developed that generate embeddings for Description Logic ontologies and use these embeddings in machine learning. One approach of generating ontologies embeddings is by first embedding the ontologies into a…
Let $\Gamma$ be a connected bridgeless metric graph, and fix a point $v$ of $\Gamma$. We define combinatorial iterated integrals on $\Gamma$ along closed paths at $v$, a unipotent generalization of the usual cycle pairing and the…
Following Penrose, we introduce a family of graph functions defined in terms of contractions of certain products of symmetric tensors along the edges of a graph. Special cases of these functions enumerate edge colorings and cycles of…
We introduce a general class $F_0$ of additive functions $f$ such that $f(p) = 1$ and prove a tight bound for exponential sums of the form $\sum_{n \le x} f(n) e(\alpha n)$ where $f \in F_0$ and $e(\theta) = \exp(2\pi i \theta)$. Both…
Razborov's flag algebra forms a powerful framework for deriving asymptotic inequalities between induced subgraph densities, underpinning many advances in extremal graph theory. This survey introduces flag algebra to computer scientists…
We prove a family of identities, expressing generating functions of powers of characteristic polynomials of permutations, as finite or infinite products. These generalize formulae first obtained in a study of the geometry/topology of…
Given a family of hypergraphs $\mathcal{H}$, we say that a hypergraph $\Gamma$ is $\mathcal{H}$-universal if it contains every $H \in \mathcal{H}$ as a subgraph. For $D, r \in \mathbb{N}$, we construct an $r$-uniform hypergraph with…
The combinatorial theory of species developed by Joyal provides a foundation for enumerative combinatorics of objects constructed from finite sets. In this paper we develop an analogous theory for the enumerative combinatorics of objects…
In a recent work, Maciej Do\l{}e\k{}ga and the author have given a formula of the expansion of the Jack polynomial $J^{(\alpha)}_\lambda$ in the power-sum basis as a non-orientability generating series of bipartite maps whose edges are…