### Discrete and Algorithmic Mathematics Red de Matemática Discreta y Algorítmica

# Recent trends

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*If you are interested in posting a short announcement, please contact Diego Ruano*.

### Recent trends IV: From a naive question to a long-standing conjecture

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. (read more)

### Recent trends III: Subsets of the integers without three term arithmetic progressions

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 (read more)

### Recent trends II: Codes, finite fields and skew polynomials

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 (read more)

### Recent trends I: Geometry, randomness and Ramsey theory

23 Feb 2024 Since its inception in the early 1900s, Ramsey theory has flourished and become a cornerstone of modern discrete mathematics (and beyond). The central question asks to determine $r(s,t)$; the minimum integer $n\in \mathbb{N}$ such that any red/blue-colouring of the edges of the complete graph $K_n$ results in either a red $K_s$ or a blue $K_t$ (read more)