9 citations · 9 across the 1 of their papers we have counts for
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Expected number of distinct part sizes in a random integer composition
Pawel Hitczenko, Gilbert Stengle
The asymptotics, as , for the expected number of distinct part sizes in a random composition of an integer n is obtained.
Random partitions with non negative rth differences
Rod Canfield, Sylvie Corteel, Pawel Hitczenko
Let be the set of partitions of n with non negative rth differences. Let be a partition chosen uniformly at random among the set . Let be a positive rth…
Stability properties for a compactly supported prescale function
V. Dobric, R. F. Gundy, P. Hitczenko
We show that if is a continuous, minimally supported prescale function, then its translates are linearly independent on any set of positive measure in the unit interval. This g…
Characterizations of orthonormal scale functions: a probabilistic approach
V. Dobric, R. F. Gundy, P. Hitczenko
The construction of a multiresolution analysis starts with specification of a scale function. The Fourier transform of this function is defined by an infinite product. The converge…
S-partitions
William M. Y. Goh, Pawel Hitczenko, Ali Shokoufandeh
This note reports on the number of s-partitions of a natural number n. In an s-partition each cell has the form for some integer k. Such partitions have potential applicati…
Average number of distinct part sizes in a random Carlitz composition
William M. Y. Goh, Pawel Hitczenko
A composition of an integer is called Carlitz if adjacent parts are different. Several characteristics of random Carlitz compsitions have been studied recently by Knopfmacher and P…