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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pram/066/03/0485-0494

    • Keywords

       

      Restricted partitions; colour partitions; quantum density of states; Gentile statistics

    • 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 partitionspks(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.

    • Author Affiliations

       

      C S Srivatsan1 M V N Murthy2 R K Bhaduri3

      1. Department of Physics, Indian Institute of Technology, Kanpur - 208 016, India
      2. The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai - 600 113, India
      3. Department of Physics, McMaster University, Ont. L8S 4M1, Hamilton, Canada

    • Dates

       
      Published
      March 2006
      Manuscript received
      19 August 2005
      Manuscript revised
      13 December 2005
      Accepted
      24 January 2006

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