75 citations · 80 across the 9 of their papers we have counts for
9 papers
Extensions of the linear bound in the Furedi-Hajnal conjecture
Martin Klazar, Adam Marcus
We present two extensions of the linear bound, due to Marcus and Tardos, on the number of 1's in an n by n 0-1 matrix avoiding a fixed permutation matrix. We first extend the linea…
On the maximal order of numbers in the "factorisatio numerorum" problem
Martin Klazar, Florian Luca
Let m(n) be the number of ordered factorizations of n in factors larger than 1. We prove that for every eps>0 n^{rho} m(n) < exp[(log n)^{1/rho}/(loglog n)^{1+eps}] holds for all i…
On identities concerning the numbers of crossings and nestings of two edges in matchings
Martin Klazar
Let M,N be two matchings on [2n]={1, 2, ..., 2n} (possibly M=N) and for a nonnegative integer l let T(M,l) be the set of those matchings on [2n+2l] which can be obtained from M by…
Non-holonomicity of the sequence
Martin Klazar
Gerhold conjectured and proved conditionally that (log n: n=1,2,...) is not a holonomic sequence. Flajolet, Gerhold and Salvy gave a proof using an analytic machinery. We give a si…
Counting set systems by weight
Martin Klazar
Applying the enumeration of sparse set partitions, we show that the number of set systems H such that the emptyset is not in H, the total cardinality of edges in H is n, and the ve…
On the least exponential growth admitting uncountably many closed permutation classes
Martin Klazar
We show that the least exponential growth of counting functions which admits uncountably many closed permutation classes lies between 2^n and (2.33529...)^n.