Author:
Banerjee Koustav,Paule Peter,Radu Cristian-Silviu,Zeng WenHuan
Abstract
AbstractLet p(n) denote the number of partitions of n. A new infinite family of inequalities for p(n) is presented. This generalizes a result by William Chen et al. From this infinite family, another infinite family of inequalities for $$\log p(n)$$
log
p
(
n
)
is derived. As an application of the latter family one, for instance obtains that for $$n\ge 120$$
n
≥
120
, $$\begin{aligned} p(n)^2>\Biggl (1+\frac{\pi }{\sqrt{24}n^{3/2}}-\frac{1}{n^2}\Biggr )p(n-1)p(n+1). \end{aligned}$$
p
(
n
)
2
>
(
1
+
π
24
n
3
/
2
-
1
n
2
)
p
(
n
-
1
)
p
(
n
+
1
)
.
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory
Reference16 articles.
1. Chen, W.Y.C., Jia, D.X.Q., Wang, L.X.: Higher order Turán inequalities for the partition function. Trans. Am. Math. Soc. 372(3), 2143–2165 (2019)
2. Chen, W.Y.C., Wang, L.X., Xie, G.Y.B.: Finite differences of the logarithm of the partition function. Math. Comput. 85, 825–847 (2016)
3. Chen, W.Y.C.: Recent developments on log-concavity and q-log-concavity of combinatorial polynomials. In: 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010). http://www.billchen.org/talks/2010-FPSAC.pdf (2010)
4. Chen, W.Y.C., Lin, B.L.S.: Congruences for the number of cubic partitions derived from modular forms. https://archive.org/details/arxiv-0910.1263
5. Collins, G.E.: Quantifier elimination for the elementary theory of real closed fields by cylindrical algebraic decomposition. Lecture Notes Comput. Sci. 33, 134–183 (1975)
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