离散数学

Constant amplitude zero-autocorrelation (CAZAC) sequences are mainly used for synchronization in communication and radar applications. The state-of-the-art proposes analytical derivation of specific families whose major limitation comes…

We study the zero-visibility cops and robbers game, where the robber is invisible to the cops until they are caught. This differs from the classic game where full information about the robber's location is known at any time. A previously…

Column generation is used alongside Dantzig-Wolfe Decomposition, especially for linear programs having a decomposable pricing step requiring to solve numerous independent pricing subproblems. We propose a filtering method to detect which…

Multicriteria Decision Making problems are important both for individuals and groups. Pairwise comparisons have become popular in the theory and practice of preference modelling and quantification. We focus on decision problems where the…

Petri nets provide accurate analogues to chemical reaction networks, with places representing individual molecules (the resources of the system) and transitions representing chemical reactions which convert educt molecules into product…

We study a large family of graph covering problems, whose definitions rely on distances, for graphs of bounded cyclomatic number (that is, the minimum number of edges that need to be removed from the graph to destroy all cycles). These…

We prove that for every integer $n > 0$ and for every alphabet $\Sigma_k$ of size $k \geq 3$, there exists a necklace of length $n$ whose Burrows-Wheeler Transform (BWT) is completely unclustered, i.e., it consists of exactly $n$ runs with…

"Metaphorical maps" or "contact representations" are visual representations of vertex-weighted graphs that rely on the geographic map metaphor. The vertices are represented by countries, the weights by the areas of the countries, and the…

We construct a family of Markov decision processes for which the policy iteration algorithm needs an exponential number of improving switches with Dantzig's rule, with Bland's rule, and with the Largest Increase pivot rule. This immediately…

In the Dominated Cluster Deletion problem, we are given an undirected graph $G$ and integers $k$ and $d$ and the question is to decide whether there exists a set of at most $k$ vertices whose removal results in a graph in which each…

We study the problem of fair division of a set of indivisible goods with connectivity constraints. Specifically, we assume that the goods are represented as vertices of a connected graph, and sets of goods allocated to the agents are…

The Frobenius Coin Problem is a classic question in mathematics: given coins of specified denominations, what is the largest amount that cannot be formed using only those coins? This brief work covers a variation of such question, posing a…

This paper introduces an optimal representation for a right-to-left parallel elliptic curve scalar point multiplication. The right-to-left approach is easier to parallelize than the conventional left-to-right approach. However, unlike the…

Edge-weighted graphs play an important role in the theory of Robinsonian matrices and similarity theory, particularly via the concept of level graphs, that is, graphs obtained from an edge-weighted graph by removing all sufficiently light…

In this paper, we introduce a class of graphs which we call average hereditary graphs. Many graphs that occur in the usual graph theory applications belong to this class of graphs. Many popular types of graphs fall under this class, such as…

A class of graphs $\cal G$ is said to be \emph{near optimal colorable} if there exists a constant $c\in \mathbb{N}$ such that every graph $G\in \cal G$ satisfies $\chi(G) \leq \max\{c, \omega(G)\}$, where $\chi(G)$ and $\omega(G)$…

We study circularity in DF0L systems, a generalization of D0L systems. We focus on two different types of circularity, called weak and strong circularity. When the morphism is injective on the language of the system, the two notions are…

Return words are a classical tool for studying shift spaces with low factor complexity. In recent years, their projection inside groups have attracted some attention, for instance in the context of dendric shift spaces, of generation of…

Dendric shift spaces simultaneously generalize codings of regular interval exchanges and episturmian shift spaces, themselves both generalizations of Sturmian words. One of the key properties enforced by dendricity is the Return Theorem. In…

A linear layout of a graph consists of a linear ordering of its vertices and a partition of its edges into pages such that the edges assigned to the same page obey some constraint. The two most prominent and widely studied types of linear…