2003/03/28 by Ville Mustonen, R. Rajesh, R Rajesh · 1 citation
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #cond-mat.stat-mech #math.CO
paper · pdf · doi:10.1088/0305-4470/36/24/304
published as Journal of Physics A, Vol 36, 6651 (2003) · 6 pages, 4 figures, revtex4
arxiv created 2003/03/28 · openalex publication_date 2003/06/05 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
The number of solid partitions of a positive integer is an unsolved problem in combinatorial number theory. In this paper, solid partitions are studied numerically by the method of exact enumeration for integers up to 50 and by Monte Carlo simulations using Wang–Landau sampling method for integers up to 8000. It is shown that lim n → ∞ ln( p 3 ( n ))/ n 3/4 = 1.79 ± 0.01, where p 3 ( n ) is the number of solid partitions of the integer n . This result strongly suggests that the MacMahon conjecture for solid partitions, though not exact, could still give the correct leading asymptotic behaviour.