The number of distinct part sizes in a random integer partition
نویسندگان
چکیده
منابع مشابه
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...
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We study the size of the rth smallest part and the rth smallest distinct part in a random integer partition. This extends the research on partitions with no small parts of Nicolas and Sárközy. – To the memory of Nicolaas Govert (Dick) de Bruijn
متن کاملAverage 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.
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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...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1995
ISSN: 0097-3165
DOI: 10.1016/0097-3165(95)90111-6