3 citations · 7 across the 6 of their papers we have counts for
6 papers
Left to right maxima in Dyck Paths
Aubrey Blecher, Arnold Knopfmacher
In a Dyck path a peak which is (weakly) higher than all the preceding peaks is called a strict (weak) left to right maximum. We obtain explicit generating functions for both weak a…
The number of distinct adjacent pairs in geometrically distributed words
Margaret Archibald, Aubrey Blecher, Charlotte Brennan +3
A sequence of geometric random variables of length is a sequence of independent and identically distributed geometric random variables () where $\math…
Smooth words and Chebyshev polynomials
Arnold Knopfmacher, Toufik Mansour, Augustine Munagi +1
A word over the alphabet is said to be {\em smooth} if there are no two adjacent letters with difference greater than 1. A word is said to be…
On the Number of Distinct Multinomial Coefficients
George E. Andrews, Arnold Knopfmacher, Burkhard Zimmermann
We study M(n), the number of distinct values taken by multinomial coefficients with upper entry n, and some closely related sequences. We show that both pP(n)/M(n) and M(n)/p(n) te…
Graphical Compositions 1: Basic Enumeration
A Knopfmacher, M E Mays
Graph compositions generalize both integer compositions and partitions of a finite set. We develop formulas, generating functions and recurrence relations for composition counting…
Combinatorics of geometrically distributed random variables: Value and position of the r-th left-to-right maximum
Arnold Knopfmacher, Helmut Prodinger
For words of length n, generated by independent geometric random variables, we consider the average value and the average position of the r-th left-to-right maximum, for fixed r an…