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We study the correlations (and alignment as a particular case) existent between the fragments originated in a decaying process when the daughter particles interact. The interaction between the particles is modeled using the potential of…
In this paper all seven-vertex type solutions of the coloured Yang-Baxter equation dependent on spectral as well as coloured parameters are given. It is proved that they are composed of five groups of basic solutions, two groups of their…
The generating function of reverse plane partitions of a fixed shape factors into a product featuring the hook-lengths of this shape. This result, which was first obtained by Stanley, can be explained bijectively using the Hillman-Grassl…
Statistical models are widely used for the investigation of complex system's behavior. Most of the models considered in the literature are formulated on regular lattices with nearest-neighbor interactions. The models with non-local…
We describe a novel Yang-Baxter integrable vertex model. From this vertex model we construct a certain class of partition functions that we show are equal to the LLT polynomials of Lascoux, Leclerc, and Thibon. Using the vertex model…
Given an arbitrary choice of two sets of nonzero Boltzmann weights for $n$-color lattice models, we provide explicit algebraic conditions on these Boltzmann weights which guarantee a solution (i.e., a third set of weights) to the…
We demonstrate the effective action scheme for the leading parton interactions and discuss the symmetry properties. The interaction kernels are particular cases of conformal symmetric two-particle kernels. There is a direct relation to the…
We state a number of related questions on the structure of perfect matchings. Those questions are inspired by and directly connected to Quantum Physics. In particular, they concern the constructability of general quantum states using modern…
We introduce and study the domain wall boundary partition function of the integrable six-vertex model with triangular boundary. We first formulate the domain wall boundary partition function with triangular boundary by using the $U_q(sl_2)$…
A biquandle is a solution to the set-theoretical Yang-Baxter equation, which yields invariants for virtual knots such as the coloring number and the state-sum invariant. A virtual biquandle enriches the structure of a biquandle by…
Based on recent results obtained by the authors on the inverse scattering method of the vector nonlinear Schr\"odinger equation with integrable boundary conditions, we discuss the factorization of the interactions of N-soliton solutions on…
Two types of Yang-Baxter systems play roles in the theoretical physics -- constant and colour dependent. The constant systems are used mainly for construction of special Hopf algebra while the colour or spectral dependent for construction…
In this paper, we initiate the study of the interplay between $k$-graphs and the Yang-Baxter equation. For this, we provide two very different perspectives. One one hand, we show that the set of all set-theoretic solutions of the…
Motivated by experiments on cell segregation, we present a two-species model of interacting particles, aiming at a quantitative description of this phenomenon. Under precise scaling hypothesis, we derive from the microscopic model a…
We consider a process in which there are two types of particles, A and B, on an infinite one-dimensional lattice. The particles hop to their adjacent sites, like the totally asymmetric exclusion process (ASEP), and have also the following…
We present the development of a new colour reconnection model in PYTHIA where the full spacetime separation between partons constrains the reconnection probability throughout the final-state radiative shower. Building upon previous ideas of…
The study of the set-theoretic solutions of the reflection equation, also known as reflection maps, is closely related to that of the Yang-Baxter maps. In this work, we construct reflection maps on various geometrical objects, associated…
It is shown how Yang-Baxter maps may be directly obtained from classical counterparts of the star-triangle relations and quantum Yang-Baxter equations. This is based on reinterpreting the latter equation and its solutions which are given in…
This paper considers aspects of a Kagome lattice system with states classified by plane partitions. Using two sets of free fermions, we rewrite the lattice in terms of two families of spin chains. In this formalism, the quantum crystals…
We construct colored lattice models whose partition functions represent symplectic and odd orthogonal Demazure characters and atoms. We show that our lattice models are not solvable, but we are able to show the existence of sufficiently…