An H-graph is one representable as the intersection graph of connected subgraphs a suitable subdivision fixed H, introduced by Biró et al. (Discrete Mathematics 100:267–279, 1992). proper if representing H can be chosen incomparable inclusion. In this paper, we focus on isomorphism problem for \(S_d\)-graphs and T-graphs, where \(S_d\) star with d rays T an arbitrary tree. Answering open Chapli...

To explain (at least qualitatively) the unconventional magnetic behavior of certain materials, the physicists have been led to formulate and to study simple mathematical models. The concepts and methods they developed in this process appear to apply to a number of important random combinatorial optimization problems, for which they have proposed remarkable formulas. Their discoveries point towa...

The notion of an adaptive landscape has proved to be a valuable concept in theoretical investigations of evolutionary change, combinatorial optimization, and the physics of disordered systems. Landscape theory has emerged as an attempt to devise suitable mathematical structures for describing the \static" properties of landscapes as well as their in uence on the dynamics of adaptation. Here we ...

This work presents a Boolean satisfiability (SAT) encoding for a special problem from combinatorial optimization. In the last years much progress has been made in the optimization of practical SAT solvers (see the SAT competition [5]). This has made SAT encodings for combinatorial problems highly attractive. In this work we propose an encoding for the combinatorial problem Magic Labeling which ...

Increasingly, discrete mathematics is influenced by connections with other fields. We give one example of a broad topic in the field of discrete mathematics that comes from the social sciences, and in particular from the theory of measurement that has been developed to put measurement, especially in the social sciences, on a firm mathematical foundation. The key concept is that of meaningful st...

SUMMARY of Dainis Zeps doctoral thesis: The theory of combinatorial maps and its use in the graph-topological computations

Given positive integers n, and p1, . . . , pr, we define a fast word combinatorial algorithm for constructing a word w = w1 · · ·wn of length n, with periods p1, . . . , pr, and on the maximal number of distinct letters. We show that the constructed word, which is unique up to word isomorphism, is a pseudo-palindrome, i.e., is a fixed point of an involutory antimorphism.

The two themes that run through Joseph A. Gallian’s service to mathematics are (a) encouraging young mathematicians and helping them to develop successful careers and (b) communicating mathematics to the widest possible audience. He was one of the early proponents of undergraduates conducting mathematical research, and his REU at Duluth, which began in 1977, is widely regarded as the premier RE...

Representation theory is a fundamental tool for studying group symmetry − geometric, analytic, or algebraic − by means of linear algebra, which has important applications to other areas of mathematics and mathematical physics. One very successful trend in this field in recent decades involves using combinatorial objects to model the representations, which allows one to apply combinatorial metho...

Positive geometries provide a modern approach for computing scattering amplitudes in variety of physical models. In order to facilitate the exploration these new geometric methods, we introduce Mathematica package called “amplituhedronBoundaries” calculating boundary structures three positive geometries: amplituhedron, momentum amplituhedron and hypersimplex. The first two are relevant planar N...