A recurrence, a determinant formula, and generating functions are presented for enumerating words with restricted letters by adjacencies. The main theorem leads to reÿnements (with up to two additional parameters) of known results on compositions, polyominoes, and permutations. Among the examples considered are (1) the introduction of the ascent variation… (More)
� Under assumptions compatible with the theory of Markov chains, we use a property of Vandermonde matrices to examine the reliability of an n-component system of production or service.
Several extensions of Blomqvist's absorption process are presented. Inherent in some of the associated distributions is a method for establishing q-identities ranging from properties of Gaussian polynomials to product expansions of basic hypergeometric series to extensions of results on Mahonian statistics. One process links the comajor index to Russian… (More)
The distribution for the number of searches needed to find k of n lost objects is expressed in terms of a refinement of the q-Eulerian polynomials, for which formulae are developed involving homogeneous symmetric polynomials. In the case when k � n and the find probability remains constant, relatively simple and efficient formulas are obtained. From our… (More)
Two inversion formulas for enumerating words in the free monoid by-adjacencies are applied in counting pairs of permutations by various statistics. The generating functions obtained involve reenements of bibasic Bessel functions. We further extend the results to nite sequences of permutations.
We expose the ties between the consecutive pattern enumeration problems as sociated with permutations, compositions, column-convex polyominoes, and words. Our perspective allows powerful methods from the contexts of compositions, column convex polyominoes, and of words to be applied directly to the enumeration of per mutations by consecutive patterns. We… (More)
The inverse of Fedou's insertion-shift bijection is used to deduce a general form for the q-exponential generating function for permutations by consecutive patterns (overlaps allowed) and inversion number from a result due to Jackson and Goulden for enumerating words by distinguished factors. Explicit q-exponential generating functions are then derived for… (More)