Discrete and algorithmic mathematics is an area that studies combinatorial and discrete structures, in particular graphs and networks, finite geometries, discrete geometric structures and combinatorial aspects in algebra and number theory.
It includes their computational and algorithmic aspects arising from the particularly natural connection of discrete mathematics with computer science.
With tools coming from analysis, topology, algebra, geometry and probability and a wide range of applications in computer science, information theory, coding theory, statistics, physics, biology and social sciences, discrete mathematics is a genuine interdisciplinary area both within mathematics and in connection with science and technology as a whole.
The main goal of this Network is to foster cooperation among the existing groups in the area in Spain, reinforcing their scientific collaboration, coordinating scientific activities and training of young researchers and increase the international visibility of the Spanish research in Discrete Mathematics.
It will reinforce the participation of female researchers and promote outreach activities for the social awareness of science and technology with particular focus on Discrete Mathematics.
25 Mar 2025
The Kunz polyhedron is a family of polyhedra whose integer points correspond to numerical semigroups. This blog post explores the connection between the geometry of the Kunz polyhedron and the combinatorial properties of the numerical semigroups it classifies.
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24 Jun 2024
Shortest path problems, where the goal is to find an optimal path between two points in the plane, are among the fundamental problems in computational geometry. These problems are crucial for a variety of applications, GPS navigation is perhaps the best-known application. However, there are numerous daily-life problems that can be solved using shortest path algorithms.
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04 May 2024
My aim is to talk about a question on numerical semigroups posed by Herbert Wilf (Wilf 1978) in the late seventies. This question deserves to be included in the gallery of easy-to-state but dangerous problems. That it is easy to state will soon become apparent.
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22 Apr 2024
Let $A\subset \lbrace 1,\ldots, N\rbrace $ be a subset without non-trivial 3-term arithmetic progressions (APs), i.e., such that the equation $a+b=2c$ only has solutions for $a,b,c\in A$ if $a=b=c$. What is the maximum size $r_3(N):=\max_{A\subset \lbrace 1,\ldots,N\rbrace \text{ without 3 APs}}(|A|)$ that we can have? This question and many similar ones have driven the development of an important part of additive combinatorics during the last century
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23 Mar 2024
Polynomials are used in virtually every area of Mathematics, and Coding Theory is not an exception. One of the most used error-correcting codes in practice are Reed-Solomon codes, which are defined as subspaces whose vectors are evaluations of polynomials (over a finite field $\mathbb{F}_q$) up to a certain degree
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