Related papers: A generalized Beraha conjecture for non-planar gra…

This paper deals with the partition function of the Ising model from statistical mechanics, which is used to study phase transitions in physical systems. A special case of interest is that of the Ising model with constant energies and…

Kochol introduced the assigning polynomial $F(G,\alpha;k)$ to count nowhere-zero $(A,b)$-flows of a graph $G$, where $A$ is a finite Abelian group and $\alpha$ is a $\{0,1\}$-assigning from a family $\Lambda(G)$ of certain nonempty vertex…

A $k$-weak bisection of a cubic graph $G$ is a partition of the vertex-set of $G$ into two parts $V_1$ and $V_2$ of equal size, such that each connected component of the subgraph of $G$ induced by $V_i$ ($i=1,2$) is a tree of at most $k-2$…

We suggest a relatively simple and totally geometric conjectural description of uncolored DAHA superpolynomials of arbitrary algebraic knots (conjecturally coinciding with the reduced stable Khovanov-Rozansky polynomials) via the flagged…

The zeroes of Goss polynomials $G_{k, \Lambda}(X)$ for $\Lambda = A \defeq \mathbb{F}_{q}[T]$ and similar lattices $\Lambda$ are studied. Generically, the zero distribution follows a simple pattern governed by the $q$-adic expansion of…

We present an efficient quantum algorithm for the exact evaluation of either the fully ferromagnetic or anti-ferromagnetic q-state Potts partition function Z for a family of graphs related to irreducible cyclic codes. This problem is…

The q-state Potts model is a fundamental framework in statistical physics and graph theory, with its partition function encoding rich information about spin configurations. The multivariate Tutte polynomial (known as the partition function…

We study quasipolynomials enumerating proper colorings, nowhere-zero tensions, and nowhere-zero flows in an arbitrary CW-complex $X$, generalizing the chromatic, tension and flow polynomials of a graph. Our colorings, tensions and flows may…

We study a log-gas on a network (a finite, simple graph) confined in a bounded subset of a local field (i.e. R, C, Q_{p} the field of p-adic numbers). In this gas, a log-Coulomb interaction between two charged particles occurs only when the…

We present exact calculations of the Potts model partition function $Z(G,q,v)$ for arbitrary $q$ and temperature-like variable $v$ on $n$-vertex strip graphs $G$ of the honeycomb lattice for a variety of transverse widths equal to $L_y$…

We put forward the concept of measure graphs. These are (possibly uncountable) graphs equipped with an action of a groupoid and a measure invariant under this action. Examples include finite graphs, periodic graphs, graphings and…

For $\textbf{r}=(r_1,\ldots,r_k)$, an $\textbf{r}$-factorization of the complete $\lambda$-fold $h$-uniform $n$-vertex hypergraph $\lambda K_n^h$ is a partition of the edges of $\lambda K_n^h$ into $F_1,\ldots, F_k$ such that $F_j$ is…

We consider the Q-state Potts model in the random-cluster formulation, defined on finite two-dimensional lattices of size L x N with toroidal boundary conditions. Due to the non-locality of the clusters, the partition function Z(L,N) cannot…

We show that every uniform state on the sphere is essentially a superposition of regular graphs. In addition, we develop a graph-based ansatz to construct trial FHQ ground states sharing the local properties of Jack polynomials. In…

Amos et al. (Discrete Appl. Math. 181 (2015) 1-10) introduced the notion of the $k$-forcing number of graph for a positive integer $k$ as the generalization of the zero forcing number of a graph. The $k$-forcing number of a simple graph…

This paper addresses a theory of R(p,q)-deformed combinatorics in discrete probability. It mainly focuses on R(p,q)-deformed factorials, binomial coefficients, Vandermonde's formula, Cauchy's formula, binomial and negative binomial…

We compute the quadratic embedding constant for complete bipartite graphs with disjoint edges removed. Moreover, we study the quadratic embedding property for theta graphs, i.e., graphs consisting of three paths with common initial points…

A graph $G$ is $k$-vertex-critical if $G$ has chromatic number $k$ but every proper induced subgraph of $G$ has chromatic number less than $k$. The study of $k$-vertex-critical graphs for graph classes is an important topic in algorithmic…

Let $\mathcal{P}$ be a graph property. A $\mathcal{P}$-coloring with at most $k$ colors is a coloring of the vertices of a simple graph $G$ such that each color class induces a graph in $\mathcal{P}$. Harary polynomials are generalizations…

We calculate the chromatic polynomials $P((G_s)_m,q)$ and, from these, the asymptotic limiting functions $W(\{G_s\},q)=\lim_{n \to \infty}P(G_s,q)^{1/n}$ for families of $n$-vertex graphs $(G_s)_m$ comprised of $m$ repeated subgraphs $H$…