E-mobility, in particular electric vehicles (EVs), play a crucial role in the energy transition. While businesses are increasingly adopting EVs, there is still a lot of opportunity to grow. One aspect of this growth is the way these vehicles are used by companies, especially when it comes to the logistics of EV charging. To encourage companies to f...
The dominating set problem (DSP) is one of the most famous problems in combinatorial optimization. It is defined as follows. For a given graph G=(V,E), a dominating set of G is a subset S⊆V such that every vertex in V∖S is adjacent to at least one vertex in S. Furthermore, the DSP is the problem of finding a minimum-size dominating set and the corr...
A multigraph G is an (s,q)-graph if every s-set of vertices in G supports at most q edges of G, counting multiplicities. Mubayi and Terry posed the problem of determining the maximum of the product of the edge-multiplicities in an (s,q)-graph on n vertices. We give an asymptotic solution to this problem for the family (s,q)=(2r,a(2r2)+ex(2r,Kr+1)−1...
We construct a family of solvable lattice models whose partition functions include p-adic Whittaker functions for general linear groups from two very different sources: from Iwahori-fixed vectors and from metaplectic covers. Interpolating between them by Drinfeld twisting, we uncover unexpected relationships between Iwahori and metaplectic Whittake...
We determine the sensitivity of a current optimal solution to a combinatorial optimization problem to cost changes in a set of elements. In a recent study, the concept of regular set tolerances has been introduced for a combinatorial optimization problem and for three types of cost functions, namely sum, product, and bottleneck. A regular set toler...
The goal of this paper is to show the existence (using probabilistic tools) of configurations of lines, boxes, and points with certain interesting combinatorial properties. (i) First, we construct a family of $n$ lines in $\mathbb{R}^3$ whose intersection graph is triangle-free of chromatic number $\Omega(n^{1/15})$. This improves the previously be...
With only a complete solution in dimension one and partially solved in dimension two, the Lenz-Ising model of magnetism is one of the most studied models in theoretical physics. An approach to solving this model in the high-dimensional case (d>4) is by modelling the magnetisation distribution with p,q-binomial coefficients. The connection between t...
We prove that the maximum number of edges in a 3-uniform linear hypergraph on $n$ vertices containing no 2-regular subhypergraph is $n{1+o(1)}$. This resolves a conjecture of Dellamonica, Haxell, & Lstrok;uczak, Mubayi, Nagle, Person, R & ouml;dl, Schacht, and Verstra & euml;te. We use this result to show that the maximum number of edges in a $3$-u...
A combinatorial game is a two player game with alternating moves and no hidden information or chance elements, such as chess, Go and Connect Four. Some games can be viewed as the sum of simpler games, where a move in the full game consists of moving in one of the terms. The temperature of a game is a measure of the urgency of the first move. This t...
We study sets of mutually orthogonal Latin rectangles (MOLR), and a natural variation of the concept of self-orthogonal Latin squares which is applicable on larger sets of mutually orthogonal Latin squares and MOLR, namely that each Latin rectangle in a set of MOLR is isotopic to each other rectangle in the set. We call such a set of MOLR co-isotop...
