Related papers: Intertwiners and \ade Lattice Models
We conjecture recurrence relations satisfied by the degrees of some linearizable lattice equations. This helps to prove linear growth of these equations. We then use these recurrences to search for lattice equations that have linear growth…
Physical strands or sheets that can be modelled as curves or surfaces embedded in three dimensions are ubiquitous in nature, and are of fundamental importance in mathematics, physics, biology and engineering. Often the physical…
We introduce a class of $n$-dimensional (possibly inhomogeneous) spin-like lattice systems presenting modulated phases with possibly different textures. Such systems can be parameterized according to the number of ground states, and can be…
Characterizing the importances (i.e., centralities) of nodes in social, biological, and technological networks is a core topic in both network science and data science. We present a linear-algebraic framework that generalizes…
We discuss basic features and new developments in recently proposed induced gauge theory solvable in any number of dimensions in the limit of infinite number of colours. Its geometrical (string) picture is clarified, using planar graph…
We study the edge transport properties of $2d$ interacting Hall systems, displaying single-mode chiral edge currents. For this class of many-body lattice models, including for instance the interacting Haldane model, we prove the…
An intertwine of a pair of matroids is a matroid such that it, but none of its proper minors, has minors that are isomorphic to each matroid in the pair. For pairs for which neither matroid can be obtained, up to isomorphism, from the other…
We introduce a model for describing the dynamics of large numbers of interacting cells. The fundamental dynamical variables in the model are sub-cellular elements, which interact with each other through phenomenological intra- and…
We introduce certain lattice sums associated with hyperplane arrangements, which are (multiple) sums running over integers, and can be regarded as generalizations of certain linear combinations of zeta-functions of root systems. We also…
In this paper we derive intertwining relations for a broad class of conservative particle systems both in discrete and continuous setting. Using the language of point process theory, we are able to derive a natural framework in which…
Lattice structures play a central role in spectral graph theory, offering analytical insight into diffusion, synchronization, and transport processes on regular discrete spaces. While their spectral properties are completely characterized…
A foundational question in the theory of linear compartmental models is how to assess whether a model is structurally identifiable -- that is, whether parameter values can be inferred from noiseless data -- directly from the combinatorics…
This paper aims to undertake an exploration of the behavior of the moduli space of line arrangements while establishing its combinatorial interplay with the incidence structure of the arrangement. In the first part, we investigate…
Fusion surface models generalize the concept of anyon chains to 2+1 dimensions, utilizing fusion 2-categories as their input. We investigate bond-algebraic dualities in these systems and show that distinct module tensor categories…
The notion of disjoint weighing matrices is introduced as a generalization of orthogonal designs. A recursive construction along with a computer search lead to some infinite classes of disjoint weighing matrices, which in turn are shown to…
Many intercalation compounds possess layered structures or inter-penetrating lattices that enable phase separation into three or more stable phases, or "stages," driven by competing intra-layer and inter-layer forces. While these structures…
Multilayer networks have become increasingly ubiquitous across diverse scientific fields, ranging from social sciences and biology to economics and international relations. Despite their broad applications, the inferential theory for…
We provide a proof of Sholander's claim (Trees, lattices, order, and betweenness, Proc. Amer. Math. Soc. 3, 369-381 (1952)) concerning the representability of collections of so-called segments by trees, which yields a characterization of…
We regard explanations as a blending of the input sample and the model's output and offer a few definitions that capture various desired properties of the function that generates these explanations. We study the links between these…
A study is made of properties of the Z(3) interface which forms between the different ordered phases of pure SU(3) gauge theory above a critical temperature. The theory is simulated on a (2+1)-D lattice at various temperatures above this…