Image partition regularity of matrices near 0 with real entries.
Image partition regularity over the integers, rationals and reals.
Image partition regularity over the reals.
Improved bounds on the length of maximal abelian square-free words.
Indestructible colourings and rainbow Ramsey theorems
We show that if a colouring c establishes ω₂ ↛ [(ω₁:ω)]² then c establishes this negative partition relation in each Cohen-generic extension of the ground model, i.e. this property of c is Cohen-indestructible. This result yields a negative answer to a question of Erdős and Hajnal: it is consistent that GCH holds and there is a colouring c:[ω₂]² → 2 establishing ω₂ ↛ [(ω₁:ω)]₂ such that some colouring g:[ω₁]² → 2 does not embed into c. It is also consistent that is arbitrarily large, and there...
Integer sequences avoiding prime pairwise sums.
Intersecting and cross-intersecting families of labeled sets.
Intersecting families in the alternating group and direct product of symmetric groups.
Intersecting systems of signed sets.
Isomorphism classes of maximal intersecting uniform families are few.
-Ramsey classes and dimensions of graphs
In this note, we introduce the notion of -Ramsey classes of graphs and we reveal connections to intersection dimensions of graphs.
La fonction de Brakemeier dans le probléme d'Erdős-Ginzburg-Ziv
Large bounded degree trees in expanding graphs.
Limit distributions for multitype branching processes of -ary search trees
Let be an integer. The so-called-ary search treeis a discrete time Markov chain which is very popular in theoretical computer science, modelling famous algorithms used in searching and sorting. This random process satisfies a well-known phase transition: when , the asymptotic behavior of the process is Gaussian, but for it is no longer Gaussian and a limit of a complex-valued martingale arises. In this paper, we consider the multitype branching process which is the continuous time version...
Lower bounds on van der Waerden numbers: randomized- and deterministic-constructive.
Macaulay posets.
Maximal flat antichains of minimum weight.
Maximal sets of numbers not containing k+1 pairwise coprime integers
Measures of sum-free intersecting families.
Minimal weight in union-closed families.