We consider four families of forests on n vertices: labeled and unlabeled forests containing rooted and unrooted trees, respectively. A forest is chosen uniformly from one of the given four families.â€¦ (More)

Here u is finite, |x| < 1 and {aj}jâ‰¥1 is a given sequence of non-negative numbers. A combinatorial interpretation of (1.1) for integer-valued sequences {aj}jâ‰¥1, is The author was partially supportedâ€¦ (More)

A random mapping ( T ; q ) of a finite set V = { 1,2, . . . , n } into itself assigns independently to each i E V its unique image j = T( i ) E V with probability 4 for i = j and with probability I-qâ€¦ (More)

and the rows and columns are arranged in decreasing order: Ï‰i,j â‰¥ Ï‰i+1,j, Ï‰i,j â‰¥ Ï‰i,j+1 for all i, j â‰¥ 1. The non-zero entries Ï‰i,j > 0 are called parts of Ï‰. Sometimes, for the sake of brevity, theâ€¦ (More)

Recent work of Brlek et al. gives a characterization of digitally convex polyominoes using combinatorics on words. From this work, we derive a combinatorial symbolic description of digitally convexâ€¦ (More)