Related papers: Growth diagrams, Domino insertion and Sign-imbalan…
We study the enumeration of diagonally and antidiagonally symmetric alternating sign matrices (DASASMs) of fixed odd order by introducing a case of the six-vertex model whose configurations are in bijection with such matrices. The model…
This article investigates second order intertwinings between semigroups of birth-death processes and discrete gradients on the space of natural integers N. It goes one step beyond a recent work of Chafa{\"i} and Joulin which establishes and…
We study the phase diagram of the one-dimensional Bose-Fermi-Hubbard model at unit filling for the scalar bosons and half filling for the $S=1/2$ fermions using quantum Monte Carlo simulations. The bare interaction between the fermions is…
We rederive the conformal anomaly for spin-1/2 fermions by a genuine Feynman graph calculation, which has not been available so far. Although our calculation merely confirms a result that has been known for a long time, the derivation is…
We study the elliptic spin-1/2 Kondo model (spin-1/2 fermions in one dimension with fully anisotropic contact interactions with a magnetic impurity) in the light of mappings to bosonic systems using the fermion-boson correspondence and…
We study growth of absolute and homological $k$-dimensional systoles of arithmetic $n$-manifolds along congruence coverings. Our main interest is in the growth of systoles of manifolds whose real rank $r > 1$. We observe, in particular,…
We study the supersymmetric extension of the gauged $ O(3) $ sigma model in $ 2+1 $ dimensions and find the supersymmetry algebra. We also discuss soliton solutions in case the Maxwell term is replaced by the Born-Infeld term. We show that…
We study the dimer and Ising models on a finite planar weighted graph with periodic-antiperiodic boundary conditions, i.e. a graph $\Gamma$ in the Klein bottle $K$. Let $\Gamma_{mn}$ denote the graph obtained by pasting $m$ rows and $n$…
We investigate an invariant, called the Serre depth, from the perspective of combinatorial commutative algebra. In this paper, we establish several properties of an analogue of the depth of Stanley-Reisner rings. In particular, we relate…
We refine known dimension formulas for spaces of cusp forms of squarefree level, determining the dimension of subspaces generated by newforms both with prescribed global root numbers and with prescribed local signs of Atkin-Lehner…
Let G be a finite graph with the non-k-order property (essentially, a uniform finite bound on the size of an induced sub-half-graph). A major result of the paper applies model-theoretic arguments to obtain a stronger version of…
Let G be a finite simple graph and let indm(G) and ordm(G) denote the induced matching number and the ordered matching number of G, respectively. We characterize all bipartite graphs G with indm(G) = ordm(G). We establish the…
Let $G$ be a real algebraic semi-simple Lie group and $\Gamma$ be the fundamental group of a compact negatively curved manifold. In this article we study the limit cone, introduced by Benoist, and the growth indicator function, introduced…
We study Turing pattern formation in a system undergoing radial growth in two dimensions. The Lengyel-Epstein two variable model is implemented in COMSOL Multiphysics and solved on domains growing at different speeds while sweeping other…
The growth of multicomponent structures in simulations and experiments often results in kinetically trapped, nonequilibrium objects. In such cases we have no general theoretical framework for predicting the outcome of the growth process.…
The Erd\H{o}s--Ko--Rado theorem is extended to designs in semilattices with certain conditions. As an application, we show the intersection theorems for the Hamming schemes, the Johnson schemes, bilinear forms schemes, Grassmann schemes,…
We define an action of the symmetric group on the set of domino tableaux, and prove that the number of domino tableaux of a given weight does not depend on the permutation of components of the last. A bijective proof of the well-known…
The equation of motion of affine Toda field theory is a coupled equation for $r$ fields, $r$ is the rank of the underlying Lie algebra. Most of the theories admit reduction, in which the equation is satisfied by fewer than $r$ fields. The…
We address a number of puzzles relating to the proposed formulae for the degeneracies of dyons in orbifold compactifications of the heterotic string to four dimensions with $N =4$ supersymmetry. The partition function for these dyons is…
To investigate hyperbinary expansions of a nonnegative integer~$n$, an edge-labeled directed graph $A(n)$ has recently been introduced. After pointing out some new simple facts about its cyclomatic number, we give a relatively simple…