Using an analytic method, we derive an alternative formula for the probability that a geometrically distributed word of length n possesses the restricted growth property. Equating our result with a previously known formula yields an algebraic identity involving alternating sums of binomial coefficients via a probabilistic argument. In addition, we consider refinements of our formula obtained by fixing the number of blocks, levels, rises, or descents.
|Number of pages||9|
|Journal||Australasian Journal of Combinatorics|
|State||Published - Jun 2012|
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics