منابع مشابه
Restricted words by adjacencies
A recurrence, a determinant formula, and generating functions are presented for enumerating words with restricted letters by adjacencies. The main theorem leads to re nements (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 on compositions, (2) the enumeration of...
متن کاملAdjacencies in Words
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 generating functions. functions. We We also ...
متن کاملWords Restricted by Patterns with at Most 2 Distinct Letters
We find generating functions for the number of words avoiding certain patterns or sets of patterns with at most 2 distinct letters and determine which of them are equally avoided. We also find exact numbers of words avoiding certain patterns and provide bijective proofs for the resulting formulae. Let [k] = {1, 2, . . . , k} be a (totally ordered) alphabet on k letters. We call the elements of ...
متن کاملUniversal cycles of classes of restricted words
It is well known that Universal Cycles (U-Cycles) of k-letter words on an n-letter alphabet exist for all k and n. In this paper, we prove that Universal Cycles exist for several restricted classes of words, including non-bijections, “equitable” words (under suitable restrictions), ranked permutations, and “passwords”. In each case, proving connectedness of the underlying DeBruijn digraph is th...
متن کاملRestricted k-ary words and functional equations
We present an algorithm for finding a system of recurrence relations for the number of k-ary words of length n that satisfy a certain set of conditions. A rewriting of these relations automatically gives a system of functional equations satisfied by the multivariate generating function that counts k-ary words by their length and the indices of the corresponding recurrence relations. We propose ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2000
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(99)00380-5