Expected Number of Distinct Part Sizes in a Random Integer Composition

The Number of Distinct Part Sizes in a Random Integer Partition

A par t i t ion of n is a mul t i se t of positive integers whose sum is n. The summands , i.e., the e lements of the mult iset , are called parts. Let 9 , be the set of all par t i t ions of n, and let P ( n ) = [ 9 , [ . Put the un i fo rm probabi l i ty measure on ~ , ; mn({A}) = 1 / P ( n ) for all h ~ , . T h e n any real va lued func t ion X~ on ~ , can be regarded as a r a n d o m variab...

Average Number of Distinct Part Sizes in a Random Carlitz Composition

A composition of an integer n is called Carlitz if adjacent parts are different. Several characteristics of random Carlitz compositions have been studied recently by Knopfmacher and Prodinger. We will complement their work by establishing asymptotics of the average number of distinct part sizes in a random Carlitz composition.

Expected Number of Local Maxima of Some Gaussian Random Polnomials

The number of distinct part sizes of some multiplicity in compositions of an Integer. A probabilistic Analysis

Random compositions of integers are used as theoretical models for many applications. The degree of distinctness of a composition is a natural and important parameter. A possible measure of distinctness is the number X of distinct parts (or components). This parameter has been analyzed in several papers. In this article we consider a variant of the distinctness: the number X m of distinct parts...

expected number of local maxima of some gaussian random polnomials