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- Title
Log-concavity of infinite product generating functions.
- Authors
Heim, Bernhard; Neuhauser, Markus
- Abstract
In the 1970s Nicolas proved that the coefficients p d (n) defined by the generating function ∑ n = 0 ∞ p d (n) q n = ∏ n = 1 ∞ 1 - q n - n d - 1 are log-concave for d = 1 . Recently, Ono, Pujahari, and Rolen have extended the result to d = 2 . Note that p 1 (n) = p (n) is the partition function and p 2 (n) = pp n is the number of plane partitions. In this paper, we invest in properties for p d (n) for general d. Let n ≥ 6 . Then p d (n) is almost log-concave for n divisible by 3 and almost strictly log-convex otherwise.
- Subjects
GENERATING functions; PARTITION functions; PARTITIONS (Mathematics)
- Publication
Research in Number Theory, 2022, Vol 8, Issue 3, p1
- ISSN
2522-0160
- Publication type
Article
- DOI
10.1007/s40993-022-00352-7