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)
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.
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)
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)
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)
1. INTRODUCTION. So, you've read your fifty page manuscript a half dozen times and you continue to stumble across annoying typos. Is there any end in sight? Just how many more times do you need to read it before you're satisfied? For purposes of discussion, let's say that your manuscript originally contained 10 errors and that, because of fatigue and a… (More)
Based on a coin-tossing scheme, a generalized Mahonian statistic is defined on absorption ring mappings and applied in obtaining combinatorial interpretations of the coefficient of q j in the expansion of > k i=1 (1+q+q 2 + } } } +q m i). In the permutation case, the statistic coincides with one studied by Han that specializes many known Mahonian statistics.