75 citations · 80 across the 9 of their papers we have counts for
8 papers · 1 filter
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 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.
Extremal problems for ordered hypergraphs: small patterns and some enumeration
Martin Klazar
We investigate extremal functions ex_e(F,n) and ex_i(F,n) counting maximum numbers of edges and maximum numbers of vertex-edge incidences in simple hypergraphs H which have n verti…