A simple 2-matching in a graph is a subgraph all of whose nodes have degree 1 or 2. A simple 2-matching is called k-restricted if every connected component has > k edges. We co...
For a prime p and a vector ¯α = (α1, . . . , αk) ∈ Zk p let f (¯α, p) be the largest n such that in each set A ⊆ Zp of n elements one can find x which has a unique repr...
We study the shape of the Young diagram λ associated via the Robinson– Schensted–Knuth algorithm to a random permutation in Sn such that the length of the longest decreasing ...
In this paper, we revisit the enumeration of directed animals using gas models. We show that there exists a natural construction of random directed animals on any directed graph t...