Recent Submissions

  • The geometry of Hermitian self-orthogonal codes 

    Ball, Simeon Michael; Vilar Algueró, Ricard (Elsevier, 2021-12-20)
    Article
    Restricted access - publisher's policy
    We prove that if n>k2 then a k-dimensional linear code of length n over Fq2 has a truncation which is linearly equivalent to a Hermitian self-orthogonal linear code. In the contrary case we prove that truncations of linear ...
  • Graph polynomials and group coloring of graphs 

    Bosek, Bartlomiej; Grytczuk, Jaroslaw; Gutowski, Grzegorz; Serra Albó, Oriol; Zajac, Mariusz (2022-05-01)
    Article
    Open Access
    Let A be an Abelian group and let G be a simple graph. We say that G is A-colorable 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 

    Drmota, Michael; Noy Serrano, Marcos; Yu, Guan-Ru (2021-08-19)
    Article
    Restricted access - publisher's policy
    Catalytic 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 Reed-Solomon code is Hermitian self-orthogonal 

    Ball, Simeon Michael; Vilar Algueró, Ricard (Institute of Electrical and Electronics Engineers (IEEE), 2022-02-09)
    Article
    Open Access
    We prove that there is a Hermitian self-orthogonal k -dimensional truncated generalised Reed-Solomon code of length n¿q2 over Fq2 if and only if there is a polynomial g¿Fq2 of degree at most (q-k)q-1 such that g+gq has ...
  • Irrational-slope versions of thompson's groups T and V 

    Burillo Puig, José; Nucinkis, Brita; Reeves, Lawrence (2022-02-11)
    Article
    Open Access
    In 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 irrational-slope Thompson's group, Publ. Mat. 65 (2021), ...
  • Limiting probabilities of first order properties of random sparse graphs and hypergraphs 

    Larrauri Borroto, Lázaro Alberto; Müller, Tobias; Noy Serrano, Marcos (2021-08-18)
    Article
    Open Access
    Let Gn be the binomial random graph G(n, p = c/n) in the sparse regime, which as is well-known undergoes a phase transition at c = 1. Lynch (Random Structures Algorithms, 1992) showed that for every first order sentence ...
  • An irrational-slope Thompson’s group 

    Burillo Puig, José; Nucinkis, Brita; Reeves, Lawrence (2021-01-01)
    Article
    Open Access
    The purpose of this paper is to study the properties of the irrational-slope 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 

    Ventura Capell, Enric; Mijares, Sebastià (2021-04-07)
    Article
    Open Access
    Rationale 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 

    Ball, Simeon Michael; Jiménez Izquierdo, Enrique (Springer Nature, 2021-05-04)
    Article
    Open Access
    Let S be a set of n points in real four-dimensional 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 

    Ventura Capell, Enric; Martino, Armando; Tointon, Matthew C.H.; Valiunas, Motiejus (2021-07-02)
    Article
    Open Access
    The ‘degree of k-step 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 

    Candela Pokorna, Pablo; Catalá, Carlos; Rué Perna, Juan José; Serra Albó, Oriol (2021-09-01)
    Article
    Restricted access - publisher's policy
    Given 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 polynomial-time reduction from the multi-graph isomorphism problem to additive codeequivalence 

    Ball, Simeon Michael; Dixon, James (2021-12-02)
    Article
    Open Access
    We present a polynomial-time reduction from the multi-graph isomorphism problem to the problem of code equivalence of additive codes over finite extensions of the field with two elements.

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