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The Bernoulli sieve: an overview
The Bernoulli sieve is a version of the classical balls-in-boxes occupancy scheme, in which
random frequencies of infinitely many boxes are produced by a multiplicative random walk …
random frequencies of infinitely many boxes are produced by a multiplicative random walk …
Extremes and gaps in sampling from a GEM random discrete distribution
J Pitman, Y Yakubovich - 2017 - projecteuclid.org
We show that in a sample of size n from a GEM(0,θ) random discrete distribution, the gaps
G_i:n:=X_n-i+1:n-X_ni:n between order statistics X_1:n≤⋯≤X_n:n of the sample, with the …
G_i:n:=X_n-i+1:n-X_ni:n between order statistics X_1:n≤⋯≤X_n:n of the sample, with the …
[HTML][HTML] On gaps and unoccupied urns in sequences of geometrically distributed random variables
This paper continues the study of gaps in sequences of n geometrically distributed random
variables, as started by Hitczenko and Knopfmacher [Gap-free samples of geometric random …
variables, as started by Hitczenko and Knopfmacher [Gap-free samples of geometric random …
[HTML][HTML] The largest missing value in a composition of an integer
In this paper we find, asymptotically, the mean and variance for the largest missing value
(part size) in a composition of an integer n. We go on to show that the probability that the …
(part size) in a composition of an integer n. We go on to show that the probability that the …
Trees with flowers: A catalog of integer partition and integer composition trees with their asymptotic analysis
RG Aíza - arxiv preprint arxiv:2402.16111, 2024 - arxiv.org
We present families of combinatorial classes described as trees with nodes that can carry
one of two types of" flowers": integer partitions or integer compositions. Two parameters on …
one of two types of" flowers": integer partitions or integer compositions. Two parameters on …
Trees with flowers: a catalog of integer partition and integer composition trees with their asymptotic analysis
R Gómez-Aíza - Boletín de la Sociedad Matemática Mexicana, 2025 - Springer
We present families of combinatorial classes described as trees with nodes that can carry
one of two types of “flowers”: integer partitions or integer compositions. Two parameters on …
one of two types of “flowers”: integer partitions or integer compositions. Two parameters on …
Locally restricted compositions IV. Nearly free large parts and gap-freeness
We define the notion of t-free for locally restricted compositions, which means roughly that if
such a composition contains a part c_i and nearby parts are at least t smaller, then c_i can …
such a composition contains a part c_i and nearby parts are at least t smaller, then c_i can …
Part sizes of smooth supercritical compositional structures
We define the notion of smooth supercritical compositional structures. Two well-known
examples are compositions and graphs of given genus. The 'parts' of a graph are the …
examples are compositions and graphs of given genus. The 'parts' of a graph are the …
Part-products of 1-free integer compositions
C Shapcott - the electronic journal of combinatorics, 2011 - emis.de
Abstract If $\vec {\lambda} $ is a composition of the positive integer $ n $, define ${\bf B}(\vec
{\lambda}) $ to be the product of the parts of $\vec {\lambda} $. We present a modified …
{\lambda}) $ to be the product of the parts of $\vec {\lambda} $. We present a modified …
[HTML][HTML] Gaps in samples of geometric random variables
In this note we continue the study of gaps in samples of geometric random variables
originated in Hitczenko and Knopfmacher [Gap-free compositions and gap-free samples of …
originated in Hitczenko and Knopfmacher [Gap-free compositions and gap-free samples of …