Abstract. In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constr...
This paper discusses investigations of sequences of natural numbers which count the orbits of an in nite permutation group on n-sets or n-tuples. It surveys known results on the g...
In this paper we consider bounded real-valued functions over the discrete cube, f : {-1, 1}n [-1, 1]. Such functions arise naturally in theoretical computer science, combinatorics...
Irit Dinur, Ehud Friedgut, Guy Kindler, Ryan O'Don...
We show that thepermanent cannot be computed by uniform constantdepth threshold circuits of size Tn, for any function T such that for all k, Tk n = o2n. More generally, we show th...
The Baxter number Bn can be written as Bn = n k=0 Θk,n−k−1 with Θk,ℓ = 2 (k + 1)2 (k + 2) k + ℓ k k + ℓ + 1 k k + ℓ + 2 k . These numbers have first appeared in the...