Ponències/Comunicacions de congressos
Recent Submissions
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On homogeneous matroid ports
(Universidad de Alcalá, 2024)
Conference lecture
Open AccessA matroid port is a clutter (antichain of sets) determined by the collection of circuits of a matroid that contain a fixed point. We study the problem of determining matroid ports all whose elements have the same size h. ... -
Enhancing mathematical research in high school
(Springer, 2012)
Conference lecture
Open AccessWe present a didactic experience in the context of enhance mathematics research in high school. The encounter of three different profiles (a skilled student, a mathematics school teacher and a researcher in mathematics) ... -
Short synchronizing words for random automata
(Curran Associates, Inc., 2023)
Conference report
Open AccessWe prove that a uniformly random automaton with n states on a 2-letter alphabet has a synchronizing word of length with high probability (w.h.p.). That is to say, w.h.p. there exists a word ¿ of such length, and a state ... -
Block statistics in subcritical graph classes
(2020)
Conference report
Open AccessWe study block statistics in subcritical graph classes; these are statistics that can be defined as the sum of a certain weight function over all blocks. Examples include the number of edges, the number of blocks, and the ... -
The rado multiplicity problem in vector spaces over finite fields
(Muni press, 2023)
Conference lecture
Open AccessWe study an analogue of the Ramsey multiplicity problem for additive structures, establishing the minimum number of monochromatic $3$-APs in $3$-colorings of $\mathbb{F}_3^n$ and obtaining the first non-trivial lower bound ... -
Product-free sets in the free group
(2023)
Conference lecture
Open AccessWe prove that product-free sets of the free group over a finite alphabet have max-imum density1/2with respect to the natural measure that assigns total weight oneto each set of irreducible words of a given length. This ... -
Chordal graphs with bounded tree-width
(Masaryk University, 2023)
Conference lecture
Open AccessGiven $t\ge 2$ and $0\le k\le t$, we prove that the number of labelled $k$-connected chordal graphs with $n$ vertices and tree-width at most $t$ is asymptotically $c n^{-5/2} \gamma^n n!$, as $n\to\infty$, for some constants ... -
Extremal families for Kruskal-Katona Theorem
(2019)
Conference report
Open AccessGiven a set of size $n$ and a positive integer $k<n$, Kruskal--Katona theorem gives the minimum size of the shadow of a family $S$ of $k$-sets of $[n]$ in terms of the cardinality of $S$. We give a characterization of the ... -
Big Ramsey degrees of 3-uniform hypergraphs
(2019)
Conference report
Open AccessGiven a countably infinite hypergraph $\mathcal R$ and a finite hypergraph $\mathcal A$, the \emph{big Ramsey degree} of $\mathcal A$ in $\mathcal R$ isthe least number $L$ such that, for every finite $k$ and every ... -
The canonical Tutte polynomial for signed graphs
(2019)
Conference report
Open AccessWe construct a new polynomial invariant for signed graphs, the trivariate Tutte polynomial, which contains among its evaluations the number of proper colorings and the number of nowhere-zero flows. In this, it parallels ... -
Additive MDS codes
(2022)
Conference report
Open AccessWe prove that an additive code over a finite field which has a few projections which are equivalent to a linear code is itself equivalent to a linear code, providing the code is not too short. -
Showing non-realizability of spheres by distilling a tree
(2021)
Conference report
Open AccessIn [Zhe20a], Hailun Zheng constructs a combinatorial 3-sphere on 16 vertices whose graph is the complete 4-partite graph K4;4;4;4. Such a sphere seems unlikely to be realizable as the boundary complex of a 4-dimensional ...
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