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A removal lemma for systems of linear equations over finite fields
(2012-01)
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
(2019-08-29)
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+b-2 , where b and i are the numbers of boundary and interior points of the convex ... -
Product of primes in arithmetic progressions
(2020-05-01)
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
(2020-10-19)
Article
Restricted access - publisher's policyLet G be a graph on n vertices and with maximum degree ¿, and let k be an integer. The k-recolouring graph of G is the graph whose vertices are k-colourings of G and where two k-colourings are adjacent if they differ at ... -
On a problem of Sárközy and Sós for multivariate linear forms
(2020-03-18)
Article
Open AccessWe 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 ... -
An Erdös–Fuchs theorem for ordered representation functions
(2020-10-28)
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 bridge-addable classes
(Canadian Mathematical Society, 2020-06-01)
Article
Restricted access - publisher's policyA class of graphs is bridge-addable 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 K4-minor-free links and link-diagrams
(2020-10-01)
Article
Open AccessWe study the class of link-types that admit a -minor-free 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 d-manifolds
(2020-03-11)
Article
Open AccessWe give superexponential lower and upper bounds on the number of coloured d-dimensional 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 error-correcting codes
(2020-10-01)
Article
Restricted access - publisher's policyLet U be a ( k-1 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 edge-colorings of trees
(2020-09-26)
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 k-edge-colourings of T mixes in polynomial time in n. The bound on the number of colours is best possible as the ... -
Sidon set systems
(2020-02-11)
Article
Open AccessA family A of k-subsets 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 k-subsets of [N] satisfies Fk(N)=(N-1k-1)+N-k and the ...
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