Let Un,p be the random unary predicate and Tk the almost sure first-order theory of Un,p under the linear ordering, where k is a positive integer and n−1/k p(n) n−1/(k+1) . F...
A periodic tree Tn consists of full n-level copies of a finite tree T. The tree Tn is labeled by random bits. The root label is chosen randomly, and the probability of two adjace...
: For a pair of integers 1F␥-r, the ␥-chromatic number of an r-uniform Ž .hypergraph Hs V, E is the minimal k, for which there exists a partition of V into subsets < <T ...
We study Galton-Watson branching processes conditioned on the total progeny to be n which are scaled by a sequence cn tending to infinity as o( √ n). It is shown that this proce...
We introduce some generalizations of a nice combinatorial problem, the central notion of which is the so-called Disease Process. Let us color independently each square of an n×n c...