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The geometry of Hermitian selforthogonal codes
(Elsevier, 20211220)
Article
Restricted access  publisher's policyWe prove that if n>k2 then a kdimensional linear code of length n over Fq2 has a truncation which is linearly equivalent to a Hermitian selforthogonal linear code. In the contrary case we prove that truncations of linear ... 
Graph polynomials and group coloring of graphs
(20220501)
Article
Open AccessLet A be an Abelian group and let G be a simple graph. We say that G is Acolorable if, for some fixed orientation of G and every edge labeling l:E(G)¿A, there exists a vertex coloring c by the elements of A such that ... 
Universal singular exponents in catalytic variable equations
(20210819)
Article
Restricted access  publisher's policyCatalytic equations appear in several combinatorial applications, most notably in the enumeration of lattice paths and in the enumeration of planar maps. The main purpose of this paper is to show that the asymptotic estimate ... 
Determining when a truncated generalised ReedSolomon code is Hermitian selforthogonal
(Institute of Electrical and Electronics Engineers (IEEE), 20220209)
Article
Open AccessWe prove that there is a Hermitian selforthogonal k dimensional truncated generalised ReedSolomon code of length n¿q2 over Fq2 if and only if there is a polynomial g¿Fq2 of degree at most (qk)q1 such that g+gq has ... 
Irrationalslope versions of thompson's groups T and V
(20220211)
Article
Open AccessIn this paper, we consider the T  and V versions, Tt and Vt , of the irrational slope Thompson group Ft considered in J. Burillo, B. Nucinkis and L. Reeves [An irrationalslope Thompson's group, Publ. Mat. 65 (2021), ... 
Limiting probabilities of first order properties of random sparse graphs and hypergraphs
(20210818)
Article
Open AccessLet Gn be the binomial random graph G(n, p = c/n) in the sparse regime, which as is wellknown undergoes a phase transition at c = 1. Lynch (Random Structures Algorithms, 1992) showed that for every first order sentence ... 
An irrationalslope Thompson’s group
(20210101)
Article
Open AccessThe purpose of this paper is to study the properties of the irrationalslope Thompson’s group Ft introduced by Cleary in [11]. We construct presentations, both finite and infinite, and we describe its combinatorial structure ... 
Onto extensions of free groups
(20210407)
Article
Open AccessRationale Cocaine addiction is a chronic relapsing disorder that lacks of an effective treatment. Isoflavones are a family of compounds present in different plants and vegetables like soybeans that share a common chemical ... 
On sets defining few ordinary solids
(Springer Nature, 20210504)
Article
Open AccessLet S be a set of n points in real fourdimensional space, no four coplanar and spanning the whole space. We prove that if the number of solids incident with exactly four points of S is less than Kn3 for some K=o(n1/7) ... 
Probabilistic nilpotence in infinite groups
(20210702)
Article
Open AccessThe ‘degree of kstep nilpotence’ of a finite group G is the proportion of the tuples (x1,…, xk+1 ¿ Gk+1 for which the simple commutator [x1, …, xk+1] is equal to the identity. In this paper we study versions of this for ... 
On Motzkin’s problem in the circle group
(20210901)
Article
Restricted access  publisher's policyGiven a subset D of the interval (0,1), if a Borel set A¿[0,1) contains no pair of elements whose difference modulo 1 is in D, then how large can the Lebesgue measure of A be? This is the analogue in the circle group of a ... 
A polynomialtime reduction from the multigraph isomorphism problem to additive codeequivalence
(20211202)
Article
Open AccessWe present a polynomialtime reduction from the multigraph isomorphism problem to the problem of code equivalence of additive codes over finite extensions of the field with two elements.