Exploració per autor "Rué Perna, Juan José"
Ara es mostren els items 54-73 de 90
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On a problem of Sárközy and Sós for multivariate linear forms
(2018-07-01)
Article
Accés obertWe prove that for pairwise co-prime numbers k1,...,kd = 2 there does not exist any infinite set of positive integers A such that the representation function rA(n) = #{(a1,...,ad) ¿ Ad : k1a1 + ... + kdad = n} becomes ... -
On a problem of Sárközy and Sós for multivariate linear forms
(2020-03-18)
Article
Accés obertWe prove that for pairwise co-prime numbers k1,…,kd=2 there does not exist any infinite set of positive integers A such that the representation function rA(n)=# {(a1,…,ad)¿Ad:k1a1+¿ +kdad=n} becomes constant for n large ... -
On a question of Sárkozy and Sós for bilinear forms
(2009-02-02)
Article
Accés restringit per política de l'editorialWe prove that if 2 ≤ k1 ≤ k2, then there is no infinite sequence $\emph{A}$ of positive integers such that the representation function r(n)=#{(a, a'): n=$k{_1}a$ + $k{_2}a'$, a,a' ∊ $\emph{A}$} is constant for n large ... -
On Motzkin’s problem in the circle group
(2021-09-01)
Article
Accés obertGiven 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 ... -
On polynomial representation functions for multivariate linear forms
(2013-11-01)
Article
Accés obertGiven an infinite sequence of positive integers A, we prove that for every nonnegative integer k the number of solutions of the equation n = a1 +· · ·+ak, a1, . . . , ak ¿ A, is not constant for n large enough. This result ... -
On strong infinite Sidon and Bh sets and random sets of integers
(2021-04-21)
Article
Accés obertA set of integers S ¿ N is an a–strong Sidon set if the pairwise sums of its elements are far apart by a certain measure depending on a, more specifically if (x + w) - (y + z) = max{xa, ya, za, wa} for every x, y, z, ... -
On the error term of the logarithm of the lcm of quadratic sequences
(2013-01-09)
Article
Accés obertWe study the logarithm of the least common multiple of the sequence of integers given by 12 + 1, 2 2 + 1, . . . , n2 + 1. Using a result of Homma [4] on the distribution of roots of quadratic polynomials modulo primes we ... -
On the expected number of perfect matchings in cubic planar graphs
(2022-01-01)
Article
Accés obertA well-known conjecture by Lovász and Plummer from the 1970s asserted that a bridgeless cubic graph has exponentially many perfect matchings. It was solved in the affirmative by Esperet et al. (Adv. Math. 2011). On the ... -
On the fractional Parts of a^n/n
(2013-09-30)
Article
Accés obertWe give various results about the distribution of the sequence {a n/n}n=1 modulo 1, where a = 2 is a fixed integer. In particular, we find and infinite subsequence A such that {a n/n}n¿A is well distributed. Also we show ... -
On the limiting distribution of the metric dimension for random forests
(2015-03-20)
Article
Accés obertThe metric dimension of a graph G is the minimum size of a subset S of vertices of G such that all other vertices are uniquely determined by their distances to the vertices in S. In this paper we investigate the metric ... -
On the number of nonzero digits of some integer sequences
(2012-06-05)
Article
Accés obertLet b = 2 be a fixed positive integer. We show for a wide variety of sequences {an}8n=1 that for most n the sum of the digits of an in base b is at least cb log n, where cb is a constant depending on b and on the sequence -
On the optimality of the uniform random strategy
(2018-01-01)
Article
Accés restringit per política de l'editorialBiased Maker-Breaker games, introduced by Chvátal and Erdos, are central to the field of positional games and have deep connections to the theory of random structures. The main questions are to determine the smallest bias ... -
Outerplanar obstructions for the vertex feedback set
(2012-07-02)
Article
Accés obertFor k = 1, let Fk be the class of graphs that contains k vertices meeting all its cycles. The minor-obstruction set for Fk is the set obs(Fk) containing all minor-minimal graphs that do not belong to Fk. We denote by Yk ... -
Pentagonal chains and annuli as models for designing nanostructures from cages
(2016-03-01)
Article
Accés obertCarbon is the most versatile of chemical elements in combining with itself or other elements to form chains, rings, sheets, cages, and periodic 3D structures. One of the perspective trends for creating new molecules of ... -
Product-free sets in the free group
(2023)
Comunicació de congrés
Accés obertWe 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 ... -
Random cubic planar graphs revisited
(Elsevier, 2016)
Altres
Accés restringit per política de l'editorialThe goal of our work is to analyze random cubic planar graphs according to the uniform distribution. More precisely, let G be the class of labelled cubic planar graphs and let gn be the number of graphs with n vertices. ... -
Random cubic planar graphs revisited
(2016-10-18)
Article
Accés obertThe goal of our work is to analyze random cubic planar graphs according to the uniform distribution. More precisely, let G be the class of labelled cubic planar graphs and let gn be the number of graphs with n vertices -
Random cubic planar maps
(2023-06-30)
Article
Accés obertWe analyse uniform random cubic rooted planar maps and obtain limiting distributions for several parameters of interest. From the enumerative point of view, we present a unified approach for the enumeration of several ... -
Random strategies are nearly optimal for generalized van der Waerden Games
(2017-08-01)
Article
Accés obertIn a (1 : q) Maker-Breaker game, one of the central questions is to find (or at least estimate) the maximal value of q that allows Maker to win the game. Based on the ideas of Bednarska and Luczak [Bednarska, M., and T. ... -
Spanning trees in random series-parallel graphs
(2016-04-01)
Article
Accés obertBy means of analytic techniques we show that the expected number of spanning trees in a connected labelled series-parallel graph on n vertices chosen uniformly at random satisfies an estimate of the form s%-n(1 + o(1)), ...
