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A removal lemma for systems of linear equations over finite fields
(201201)
Article
Open AccessWe prove a removal lemma for systems of linear equations over finite fields: let X1, . . . , Xm be subsets of the finite field Fq and let A be a (k × m) matrix with coefficients in Fq and rank k; if the linear system Ax = ... 
Triangulations and a discrete Brunn–Minkowski inequality in the plane
(20190829)
Article
Open AccessFor a set A of points in the plane, not all collinear, we denote by tr(A) the number of triangles in a triangulation of A, that is, tr(A)=2i+b2 , where b and i are the numbers of boundary and interior points of the convex ... 
Product of primes in arithmetic progressions
(20200501)
Article
Open AccessWe prove that, for all q=2 and for all invertible residue classes a modulo q, there exists a natural number n=(650q)9 that is congruent to a modulo q and that is the product of exactly three primes, all of which are below ... 
Frozen (¿ + 1)colourings of bounded degree graphs
(20201019)
Article
Restricted access  publisher's policyLet G be a graph on n vertices and with maximum degree ¿, and let k be an integer. The krecolouring graph of G is the graph whose vertices are kcolourings of G and where two kcolourings are adjacent if they differ at ... 
On a problem of Sárközy and Sós for multivariate linear forms
(20200318)
Article
Open AccessWe prove that for pairwise coprime 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 ... 
An Erdös–Fuchs theorem for ordered representation functions
(20201028)
Article
Open AccessLetk=2 be a positive integer. We study concentration results for the ordered representationfunctionsr=k(A, n) = #{(a1= ··· =ak)¿ Ak:a1+···+ak=n}andr<k(A, n) = #{(a1<···<ak)¿ Ak:a1+···+ak=n}for any infinite set ... 
Local convergence and stability of tight bridgeaddable classes
(Canadian Mathematical Society, 20200601)
Article
Restricted access  publisher's policyA class of graphs is bridgeaddable if given a graph G in the class, any graph obtained by adding an edge between two connected components of G is also in the class. The authors recently proved a conjecture of McDiarmid, ... 
Structure and enumeration of K4minorfree links and linkdiagrams
(20201001)
Article
Open AccessWe study the class of linktypes that admit a minorfree diagram, i.e., they can be projected on the plane so that the resulting graph does not contain any subdivision of . We prove that is the closure of a subclass of ... 
On the number of coloured triangulations of dmanifolds
(20200311)
Article
Open AccessWe give superexponential lower and upper bounds on the number of coloured ddimensional triangulations whose underlying space is an oriented manifold, when the number of simplices goes to infinity and d=3 is fixed. In the ... 
On varieties defined by large sets of quadrics and their application to errorcorrecting codes
(20201001)
Article
Restricted access  publisher's policyLet U be a ( k1 2  1)dimensional subspace of quadratic forms defined on F k with the property that U does not contain any reducible quadratic form. Let V (U) be the points of PG(k  1, F) which are zeros of all quadratic ... 
The Glauber dynamics for edgecolorings of trees
(20200926)
Article
Restricted access  publisher's policyLet T be a tree on n vertices and with maximum degree ¿. We show that for k = ¿ + 1 the Glauber dynamics for kedgecolourings of T mixes in polynomial time in n. The bound on the number of colours is best possible as the ... 
Sidon set systems
(20200211)
Article
Open AccessA family A of ksubsets of {1,2,…,N} is a Sidon system if the sumsets A+B, A,B¿A are pairwise distinct. We show that the largest cardinality Fk(N) of a Sidon system of ksubsets of [N] satisfies Fk(N)=(N1k1)+Nk and the ...