The Bernoulli sieve: an overview

A Gnedin, A Iksanov… - Discrete Mathematics & …, 2010‏ - dmtcs.episciences.org
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 …

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 …

[HTML][HTML] On gaps and unoccupied urns in sequences of geometrically distributed random variables

G Louchard, H Prodinger - Discrete Mathematics, 2008‏ - Elsevier
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 …

[HTML][HTML] The largest missing value in a composition of an integer

M Archibald, A Knopfmacher - Discrete mathematics, 2011‏ - Elsevier
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 …

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 …

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 …

Locally restricted compositions IV. Nearly free large parts and gap-freeness

E Bender, R Canfield, Z Gao - Discrete Mathematics & …, 2012‏ - dmtcs.episciences.org
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 …

Part sizes of smooth supercritical compositional structures

EA Bender, Z Gao - Combinatorics, Probability and Computing, 2014‏ - cambridge.org
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 …

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 …

[HTML][HTML] Gaps in samples of geometric random variables

WMY Goh, P Hitczenko - Discrete mathematics, 2007‏ - Elsevier
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 …