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Additive volume of sets contained in few arithmetic progressions
(De Gruyter, 2019-03-06)
Article
Open AccessA conjecture of Freiman gives an exact formula for the largest volume of a finite set A of integers with given cardinality k=|A| and doubling T=|2A|. The formula is known to hold when T=3k-4, for some small range over 3k-4 ... -
Towards 3n - 4 in groups of prime order
(2023-06-16)
Article
Open AccessWe show that if A is a subset of a group of prime order p such that |2.Al < 2.7652|Al and 10 < |A| < 1.25 - 10-®p, then A is contained in an arithmetic progression with at most 2A - [Al + 1 terms, and 2.4 contains an ... -
Caracteritzant els codis de Gauss: només cal girar la cantonada
(2020-02-05)
Article
Open AccessAquest document està dedicat a la història, les motivacions i algunes solu-cions alproblema dels codis de Gauss.Una corba tancada al pla pot contenir punts d’autointersecció; en suposem unnombre finit, suposem els talls ... -
Enumeration of chordal planar graphs and maps
(2023-01-01)
Article
Open AccessWe determine the number of labelled chordal planar graphs with n vertices, which is asymptotically for a constant and . We also determine the number of rooted simple chordal planar maps with n edges, which is asymptotically ... -
Relative order and spectrum in free and related groups
(2022-12-19)
Article
Open AccessWe consider a natural generalization of the concept of order of an element in a group: an element g ¿ G is said to have order k in a subgroup H (resp., in a coset Hu) of a group G if k is the first strictly positive integer ... -
Autòmats de Stallings, un camí d'anada i tornada
(2022-12-14)
Article
Open AccessEn aquest article revisem algunes de les propietats fonamentals del grup lliure i fem una exposició detallada de la teoria dels autòmats de Stallings, una interpretació geomètrica dels seus subgrups que ha estat (i segueix ... -
Normal limiting distributions for systems of linear equations in random sets
(Elsevier, 2022-09-15)
Article
Open AccessWe consider the binomial random set model where each element in is chosen independently with probability . We show that for essentially all regimes of p and very general conditions for a matrix A and a column vector b, the ... -
A list of applications of stallings automata
(2022-11-22)
Article
Open AccessThis survey is intended to be a fast (and reasonably updated) reference for the theory of Stallings automata and its applications to the study of subgroups of the free group, with the main accent on algorithmic aspects. ... -
Grassl–Rötteler cyclic and consta-cyclic MDS codes are generalised Reed–Solomon codes
(Springer, 2022-12-31)
Article
Open AccessWe prove that the cyclic and constacyclic codes constructed by Grassl and Rötteler in International Symposium on Information Theory (ISIT), pp. 1104–1108 (2015) are generalised Reed–Solomon codes. This note can be considered ... -
Irreducibility of the Tutte polynomial of an embedded graph
(2022-12-19)
Article
Open AccessWe prove that the ribbon graph polynomial of a graph embedded in an orientable surface is irreducible if and only if the embedded graph is neither the disjoint union nor the join of embedded graphs. This result is analogous ... -
On additive MDS codes over small fields
(American Institute of Mathematical Sciences, 2022)
Article
Open AccessLet $ C $ be a $ (n,q^{2k},n-k+1)_{q^2} $ additive MDS code which is linear over $ {\mathbb F}_q $. We prove that if $ n \geq q+k $ and $ k+1 $ of the projections of $ C $ are linear over $ {\mathbb F}_{q^2} $ then $ C $ ... -
Positive Plücker tree certificates for non-realizability
(2022-01-24)
Article
Open AccessWe introduce a new method for finding a non-realizability certificate of a simplicial sphere S: we exhibit a monomial combination of classical 3-term Pl¨ucker relations that yields a sum of products of determinants that ...
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