Average Number of Distinct Part Sizes in a Random Carlitz Composition

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.

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...

a survey of translation of metaphors in holy quran – part 20&21

چکیده ندارد.

Random partitions with restricted part sizes

For a subsetS of positive integers let (n,S)be the set of partitions ofn into summands that are elements of S. For every λ ∈ (n,S), let Mn(λ) be the number of parts, with multiplicity, that λ has. Put a uniform probability distribution on (n,S), and regardMn as a random variable. In this paper the limiting density of the (suitably normalized) random variableMn is determined for sets that are su...

On the average number of sharp crossings of certain Gaussian random polynomials