Integer partitions and exclusion statistics

被引：22

作者：

Comtet, Alain ^{[1
]}

Majumdar, Satya N.

Ouvry, Stephane

机构：

[1] Univ Paris 11, Lab Phys Theor & modeles Statist, CNRS, YNR 8626, F-91405 Orsay, France

[2] Inst Poincare, F-75005 Paris, France

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2007年 / 40卷 / 37期

关键词：

D O I：

10.1088/1751-8113/40/37/004

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We provide a combinatorial description of exclusion statistics in terms of minimal difference p partitions. We compute the probability distribution of the number of parts in a random minimal p partition. It is shown that the bosonic point p = 0 is a repulsive fixed point for which the limiting distribution has a Gumbel form. For all positive p, the distribution is shown to be Gaussian.

引用

页码：11255 / 11269

页数：15

共 50 条

[31] The Minimal Excludant in Integer Partitions
Andrews, George E.
Newman, David
JOURNAL OF INTEGER SEQUENCES, 2020, 23 (02)
[32] CONSECUTIVE-INTEGER PARTITIONS
GUERIN, EE
ARS COMBINATORIA, 1995, 39 : 255 - 260
[33] Integer partitions and binary trees
Schmidt, F
ADVANCES IN APPLIED MATHEMATICS, 2002, 28 (3-4) : 592 - 601
[34] Stirling numbers and integer partitions
Merca, Mircea
QUAESTIONES MATHEMATICAE, 2016, 39 (04) : 457 - 469
[35] Strongly intersecting integer partitions
Borg, Peter
DISCRETE MATHEMATICS, 2014, 336 : 80 - 84
[36] Integer partitions detect the primes
Craig, William
van Ittersum, Jan-Willem
Ono, Ken
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 2024, 121 (39)
[37] On the Distribution of Multiplicities in Integer Partitions
Dimbinaina Ralaivaosaona
Annals of Combinatorics, 2012, 16 : 871 - 889
[38] An expansion for the number of partitions of an integer
Stella Brassesco
Arnaud Meyroneinc
The Ramanujan Journal, 2020, 51 : 563 - 592
[39] The lattice of partitions of a positive integer
Baransky, V. A.
Koroleva, T. A.
DOKLADY MATHEMATICS, 2008, 77 (01) : 72 - 75
[40] PERMUTATION STATISTICS AND PARTITIONS
GARSIA, AM
GESSEL, I
ADVANCES IN MATHEMATICS, 1979, 31 (03) : 288 - 305

← 1 2 3 4 5 →