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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.
Based Based on on two two inversion inversion formulas formulas for for enumerating enumerating words words in in the the free free monoid monoid by by adjacencies, adjacencies, we we present present a a new new approach approach to to a a class class of of permutation permutation problems problems having having Eulerian-type Eulerian-type generating… (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.
As motivation for our designs, first consider the identity 1=0 Next, imagine inserting an' bi in the /th term of the sum and replacing 2' by (a + b)n The result is the binomial theorem. Our objective here is to examine the effect of an analogous "pollination" of Vander-monde's identity (nt) (1) Guided by our binomial theorem example, we slip four letters… (More)