Counting pattern-free set partitions. II: Noncrossing and other hypergraphs.
Counting set systems by weight.
Generalized Davenport-Schinzel sequences: Results, problems, and applications.
On growth rates of permutations, set partitions, ordered graphs and other objects.
On growth rates of closed permutation classes.
Counting Keith numbers.
Prvočísla obsahují libovolně dlouhé aritmetické posloupnosti
A general upper bound in extremal theory of sequences
We investigate the extremal function which, for a given finite sequence over symbols, is defined as the maximum length of a sequence of integers such that 1) , 2) implies and 3) contains no subsequence of the type . We prove that is very near to be linear in for any fixed of length greater than 4, namely that Here is the length of and is the inverse to the Ackermann function and goes to infinity very slowly. This result extends the estimates in [S] and [ASS] which...
Two results on a partial ordering of finite sequences
In the first part of the paper we are concerned about finite sequences (over arbitrary symbols) for which . The function measures the maximum length of finite sequences over symbols which contain no subsequence of the type . It follows from the result of Hart and Sharir that the containment is a (minimal) obstacle to . We show by means of a construction due to Sharir and Wiernik that there is another obstacle to the linear growth. In the second part of the paper we investigate whether...
On some arithmetic properties of polynomial expressions involving Stirling numbers of the second kind
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