, Volume 66, Issue 3, pp 485-494
First online:
Gentile statistics and restricted partitions
- C. S. SrivatsanAffiliated withDepartment of Physics, Indian Institute of Technology
- , M. V. N. MurthyAffiliated withThe Institute of Mathematical Sciences
- , R. K. BhaduriAffiliated withDepartment of Physics, McMaster University
Abstract
In a recent paper (Tranet al, Ann. Phys.311, 204 (2004)), some asymptotic number theoretical results on the partitioning of an integer were derived exploiting its connection to the quantum density of states of a many-particle system. We generalise these results to obtain an asymptotic formula for therestricted or coloured partitionsp k s (n), which is the number of partitions of an integern into the summand of sth powers of integers such that each power of a given integer may occur utmostk times. While the method is not rigorous, it reproduces the well-known asymptotic results fors = 1 apart from yielding more general results for arbitrary values ofs.
Keywords
Restricted partitions colour partitions quantum density of states Gentile statisticsConcepts found in this article
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- Title
- Gentile statistics and restricted partitions
- Journal
-
Pramana
Volume 66, Issue 3 , pp 485-494
- Cover Date
- 2006-03
- DOI
- 10.1007/BF02704492
- Print ISSN
- 0304-4289
- Online ISSN
- 0973-7111
- Publisher
- Springer India
- Additional Links
- Topics
- Keywords
-
- Restricted partitions
- colour partitions
- quantum density of states
- Gentile statistics
- Industry Sectors
- Authors
-
- C. S. Srivatsan (1)
- M. V. N. Murthy (2)
- R. K. Bhaduri (3)
- Author Affiliations
-
- 1. Department of Physics, Indian Institute of Technology, 208 016, Kanpur, India
- 2. The Institute of Mathematical Sciences, CIT Campus, Taramani, 600 113, Chennai, India
- 3. Department of Physics, McMaster University, Ont. L8S 4M1, Hamilton, Canada