Universidad de Cantabria

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19942026

most citedPlanck 2015 results. XIII. Cosmological parameters

10.6k citations

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60 papers · 1 filter

math.CO2025

Covering radii of $3$ -zonotopes and the shifted Lonely Runner Conjecture

David Alcántara, Francisco Criado, Francisco Santos

We show that the shifted Lonely Runner Conjecture (sLRC) holds for 5 runners. We also determine that there are exactly 3 primitive tight instances of the conjecture, only two of wh…

math.CO2024★ 2 cited

Linearly-exponential checking is enough for the Lonely Runner Conjecture and some of its variants

Romanos Diogenes Malikiosis, Francisco Santos, Matthias Schymura

Tao (2018) showed that in order to prove the Lonely Runner Conjecture (LRC) up to $n + 1$ runners it suffices to consider positive integer velocities in the order of $n^{O (n^{2})}$ . Us…

math.CO2023

Ewald's Conjecture and integer points in algebraic and symplectic toric geometry

Luis Crespo, Álvaro Pelayo, Francisco Santos

We solve several open problems concerning integer points of polytopes arising in symplectic and algebraic geometry. In this direction we give the first proof of a broad case of Ewa…

math.CO2023★ 14 cited

Celebrating Loday's Associahedron

Vincent Pilaud, Francisco Santos, Günter M. Ziegler

We survey Jean-Louis Loday's vertex description of the associahedron, and its far reaching influence in combinatorics, discrete geometry and algebra. We present in particular four…

math.CO2022★ 3 cited

Realizations of multiassociahedra via rigidity

Luis Crespo Ruiz, Francisco Santos

Let $Δ_{k} (n)$ denote the simplicial complex of $(k + 1)$ -crossing-free subsets of edges in $(2 [ n ])$ . Here $k, n \in N$ and $n \geq 2 k + 1$ . Jonsson (2003) proved that (negle…

math.CO2022★ 1 cited

Many regular triangulations and many polytopes

Arnau Padrol, Eva Philippe, Francisco Santos

We show that for fixed $d > 3$ and $n$ growing to infinity there are at least $(n!)^{d - 2 \pm o (1)}$ different labeled combinatorial types of $d$ -polytopes with $n$ vertices. This is…