Add to ORKGA composition of a positive integer n is a finite sequence of positive integers a1, a2,..., ak such that a1 + a2 + · · · + ak = n. Let d be a fixed nonnegative integer. We say that we have an ascent of size d or more at position i, if ai+1 ≥ ai + d. We study the average position, initial height and end height of the first ascent of size d or more in compositions of n as n → ∞
A “composition” of an integer n is a tuple of positive integers that sum to n. Thus the set of all c...
20 pagesFreiman and Scourfield proved that any large enough integer can be written as a sum of a cer...
An arithmetic progression is a sequence of numbers such that the difference between the consecutive ...
A composition of a positive integer $n$ is a finite sequence of positive integers $a_1, a_2, \ldots,...
A composition of a positive integer n is a finite sequence of positive integers a1, a2,..., ak such ...
Abstract. A partition of a positive integer n is a finite sequence of positive integers a1, a2,..., ...
Abstract. We consider words or strings of characters a1a2a3... an of length n, where the letters ai ...
In this paper, compositions of n are studied. These are sequences of positive integers (σi) k i=1 wh...
CombinatoricsWe consider compositions of n, i.e., sequences of positive integers (or parts) (σi)i=1k...
A composition of n ∈ N is an ordered collection of one or more positive integers whose sum is n. The...
Abstract. For a fixed integer base b ≥ 2, we consider the number of compositions of 1 into a given n...
AbstractLet π=(π1, π2,…,πn) denote a permutation of Zn = {1, 2,…, n}. The pair (πi, πi+1) is a rise ...
Abstract. For a fixed integer base b ≥ 2, we consider the number of compositions of 1 into a given n...
AbstractLetn = (a1.a2 … aN) denote a sequence of integers ai={1.2.…n}. A rise is a part ai.ai+1 with...
When is the average of sums of powers of integers itself a sum of the first n integers raised to a p...
A “composition” of an integer n is a tuple of positive integers that sum to n. Thus the set of all c...
20 pagesFreiman and Scourfield proved that any large enough integer can be written as a sum of a cer...
An arithmetic progression is a sequence of numbers such that the difference between the consecutive ...
A composition of a positive integer $n$ is a finite sequence of positive integers $a_1, a_2, \ldots,...
A composition of a positive integer n is a finite sequence of positive integers a1, a2,..., ak such ...
Abstract. A partition of a positive integer n is a finite sequence of positive integers a1, a2,..., ...
Abstract. We consider words or strings of characters a1a2a3... an of length n, where the letters ai ...
In this paper, compositions of n are studied. These are sequences of positive integers (σi) k i=1 wh...
CombinatoricsWe consider compositions of n, i.e., sequences of positive integers (or parts) (σi)i=1k...
A composition of n ∈ N is an ordered collection of one or more positive integers whose sum is n. The...
Abstract. For a fixed integer base b ≥ 2, we consider the number of compositions of 1 into a given n...
AbstractLet π=(π1, π2,…,πn) denote a permutation of Zn = {1, 2,…, n}. The pair (πi, πi+1) is a rise ...
Abstract. For a fixed integer base b ≥ 2, we consider the number of compositions of 1 into a given n...
AbstractLetn = (a1.a2 … aN) denote a sequence of integers ai={1.2.…n}. A rise is a part ai.ai+1 with...
When is the average of sums of powers of integers itself a sum of the first n integers raised to a p...
A “composition” of an integer n is a tuple of positive integers that sum to n. Thus the set of all c...
20 pagesFreiman and Scourfield proved that any large enough integer can be written as a sum of a cer...
An arithmetic progression is a sequence of numbers such that the difference between the consecutive ...