K. Banerjee,
Invariants of the quartic binary form and proofs of Chen's
conjectures for partition function inequalities,
https://www3.risc.jku.at/publications/download/risc_6615/Chen.pdf.
PDF
K. Banerjee,
New asymptotics and inequalities related to the partition function,
Doctoral Thesis, 2022.
PDF
K. Banerjee,
A unified framework to prove multiplicative inequalities for the partition function,
Adv. in Appl. Math. 152 (2024) Paper No. 102590.
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K. Banerjee, P. Paule, C.S. Radu and W. Zeng,
New inequalities for p(n) and logp(n),
Ramanujan J 61 (2023) 1295每1338.
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K. Banerjee, P. Paule, C.S. Radu and C. Schneider,
Error bounds for the asymptotic expansion of the partition function,
arXiv:2209.07887.
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B. Benfield,
Long Concavity of the Power Partition Function,
Master Thesis, 2020.
PDF
W.Y.C. Chen,
The spt-function of Andrews,
In: A. Claesson, M. Dukes, S. Kitaev, D. Manlove and K. Meeks (eds.),
Surveys in Combinatorics 2017, 141-203,
Cambridge Univ. Press, Cambridge, 2017.
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W.Y.C. Chen, D.X.Q. Jia and L.X.W. Wang,
Higher order Tur芍n inequalities for the partition function,
Trans. Amer. Math. Soc. 372 (2019) 2143-2165.
PDF
W.Y.C. Chen, L.X.W. Wang and G.Y.B. Xie,
Finite differences of the logarithm of the partition function,
Math. Comp. 85(298) (2016) 825每847.
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W.Y.C. Chen and K.Y. Zheng,
The log-behavior of $\sqrt[n]{p(n)}$ and $\sqrt[n]{p(n)/n}$,
Ramanujan J. 44 (2017) 281-299.
PDF
S. DeSalvo and I. Pak,
Log-concavity of the partition function,
Ramanujan J 38 (2015) 61每73.
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K. Gajdzica,
Log-concavity of the restricted partition function $p_A(n,k)$
and the new Bessenrodt-Ono type inequality,
arXiv:2206.04752.
PDF
K. Gajdzica,
Restricted partition functions and the $r$-log-concavity of quasi-polynomial-like functions,
arXiv:2305.00085.
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Q.-H. Hou and Z.-R. Zhang,
$r$-log-concavity of partition functions,
Ramanujan J. 48(1) (2019) 117每129.
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D.X.Q. Jia and L.X.W. Wang,
Determinantal inequalities for the partition function,
Proc. Roy. Soc. Edinburgh Sect. A 150(3) (2020) 1451每1466.
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J. Lindsay, T. Mansour and M. Shattuck,
A new combinatorial interpretation of a $q$-analogue of the Lah numbers,
J. Comb. 2(2) (2011) 245每264.
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E.Y.S. Liu and H.W.J. Zhang,
Inequalities for the overpartition function,
Ramanujan J. 54(3) (2021) 485每509.
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M. Merca and J. Katriel,
A general method for proving the non-trivial linear homogeneous partition inequalities,
Ramanujan J. 51(2) (2020) 245每266.
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G. Mukherjee,
Log-convexity and the overpartition function,
Ramanujan J. 60(2) (2023) 517每531.
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G. Mukherjee,
Inequalities for higher order differences of the logarithm of the overpartition function and a problem of Wang-Xie-Zhang. (English summary)
Res. Number Theory 9(1) (2023) Paper No. 9.
PDF
G. Mukherjee,
Inequalities for the overpartition function arising from determinants,
Adv. in Appl. Math. 152 (2024) Paper No. 102598, 16 pp.
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G. Mukherjee,
Asymptotic Growth of $(-1)^{r} {\Delta}^r \log \sqrt[n]{\overline{p}(n)/n^{\alpha}}$ and
the Reverse Higher Order Tur\'an Inequalities for $\sqrt[n]{\overline{p}(n)/n^{\alpha}}$,
arXiv:2401.05522.
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G. Mukherjee, H.W.J. Zhang and Y. Zhong,
Higher order log-concavity of the overpartition function and its consequences,
Proc. Edinb. Math. Soc. (2) 66(1) (2023) 164每181.
PDF
Z.-W. Sun,
On a sequence involving sums of primes,
Bull. Aust. Math. Soc. 88(2) (2013) 197每205.
PDF
E.X.W. Xia,
On the log-concavity of the sequence $\{\sqrt[n]{S_n}\}_n^{\infty}=1$
for some combinatorial sequences {Sn}﹢n=0,
Proc. Roy. Soc. Edinburgh Sect. A 148(4) (2018) 881每892.
PDF
L.X.W. Wang, G.Y.B. Xie and A.Q. Zhang,
Finite difference of the overpartition function,
Adv. in Appl. Math. 92 (2018) 51每72.
PDF
L.X.W. Wang and E.Y.Y. Yang,
Laguerre inequalities for discrete sequences,
Adv. in Appl. Math. 139 (2022) 102357.
PDF
Y. Wang and B. Zhu,
Proofs of some conjectures on monotonicity of number-theoretic and combinatorial sequences,
Sci. China Math. 57(11) (2014) 2429每2435.
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