Add to ORKGLet A be any set of positive integers and n ∈ N. A composition of n with parts in A is an ordered collection of one or more elements in A whose sum is n. We derive generating functions for the number of compositions of n with m parts in A that have r occurrences of 3-letter patterns formed by two (adjacent) instances of levels, rises and drops. We also derive asymptotics for the number of compositions of n that avoid a given pattern. Finally, we obtain the generating function for the number of k-ary words of length m which contain a prescribed number of occurrences of a given pattern as a special case of our results. 1
A One-Stop Source of Known Results, a Bibliography of Papers on the Subject, and Novel Research Dire...
Integer compositions are ordered sequences of positive integers that sum up to a given integer. We u...
Integer compositions are ordered sequences of positive integers that sum up to a given integer. We u...
A composition of a nonnegative integer n is a sequence of positive integers whose sum is n.A composi...
A composition of a nonnegative integer n is a sequence of positive integers whose sum is n.A composi...
A composition of a nonnegative integer n is a sequence of positive integers whose sum is n. A compos...
A composition of a nonnegative integer n is a sequence of positive integers whose sum is n. A compos...
A composition of a nonnegative integer n is a sequence of positive integers whose sum is n. A compos...
Let ℕ be the set of all positive integers and let A be any ordered subset of ℕ. Recently, Heubach an...
A composition of n ∈ N is an ordered collection of one or more positive integers whose sum is n. The...
Enumeration of pattern avoiding compositions of numbers Abstract The aim of this work was to find so...
A composition of an integer n is a tuple of positive integers that sum up to n. Our study began with...
A composition of an integer n is a tuple of positive integers that sum up to n. Our study began with...
A composition of a nonnegative integer n is a sequence of positive integers whose sum is n.A composi...
A composition of a nonnegative integer n is a sequence of positive integers whose sum is n.A composi...
A One-Stop Source of Known Results, a Bibliography of Papers on the Subject, and Novel Research Dire...
Integer compositions are ordered sequences of positive integers that sum up to a given integer. We u...
Integer compositions are ordered sequences of positive integers that sum up to a given integer. We u...
A composition of a nonnegative integer n is a sequence of positive integers whose sum is n.A composi...
A composition of a nonnegative integer n is a sequence of positive integers whose sum is n.A composi...
A composition of a nonnegative integer n is a sequence of positive integers whose sum is n. A compos...
A composition of a nonnegative integer n is a sequence of positive integers whose sum is n. A compos...
A composition of a nonnegative integer n is a sequence of positive integers whose sum is n. A compos...
Let ℕ be the set of all positive integers and let A be any ordered subset of ℕ. Recently, Heubach an...
A composition of n ∈ N is an ordered collection of one or more positive integers whose sum is n. The...
Enumeration of pattern avoiding compositions of numbers Abstract The aim of this work was to find so...
A composition of an integer n is a tuple of positive integers that sum up to n. Our study began with...
A composition of an integer n is a tuple of positive integers that sum up to n. Our study began with...
A composition of a nonnegative integer n is a sequence of positive integers whose sum is n.A composi...
A composition of a nonnegative integer n is a sequence of positive integers whose sum is n.A composi...
A One-Stop Source of Known Results, a Bibliography of Papers on the Subject, and Novel Research Dire...
Integer compositions are ordered sequences of positive integers that sum up to a given integer. We u...
Integer compositions are ordered sequences of positive integers that sum up to a given integer. We u...