# Asymptotic formulae in combinatory analysis

@article{HardyAsymptoticFI, title={Asymptotic formulae in combinatory analysis}, author={Gordon H. Hardy and Srinivasa Ramanujan}, journal={Journal of The London Mathematical Society-second Series}, volume={17}, pages={75-115} }

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## 686 Citations

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The equidistribution of Hodge numbers for Hilbert schemes of suitable smooth projective surfaces is deduced and a contemporary example of its legacy in topology is presented.

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- 2022

. Recent work of Cesana, Craig and the third author shows that the trace of plane partitions is asymptotically equidistributed in residue classes mod b . Applying a technique of the ﬁrst two authors…

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- MathematicsAnnals of Combinatorics
- 2022

. Let j, n be even positive integers, and let p j ( n ) denote the number of partitions with BG-rank j , and p j ( a, b ; n ) to be the number of partitions with BG-rank j and 2-quotient rank…

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- Mathematics
- 2022

. Let p ( n ) denote the overpartition funtion. This paper presents the 2-log-concavity property of p ( n ) by considering a more general inequality of the following form holds for all n ≥ 42.

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- Materials ScienceResults in Mathematics
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Recently, Juyal, Maji, and Sathyanarayana have studied a Lambert series associated with a cusp form over the full modular group and the Möbius function. In this paper, we investigate the Lambert…

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- MathematicsForum of Mathematics, Sigma
- 2022

Abstract Recent works at the interface of algebraic combinatorics, algebraic geometry, number theory and topology have provided new integer-valued invariants on integer partitions. It is natural to…

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- MathematicsInternational Journal of Number Theory
- 2022

. The average size of the “smallest gap” of a partition was studied by Grabner and Knopfmacher in 2006. Recently, Andrews and Newman, motivated by the work of Fraenkel and Peled, studied the concept…

### Some generating functions and inequalities for the andrews–stanley partition functions

- MathematicsProceedings of the Edinburgh Mathematical Society
- 2021

Abstract Let $\mathcal {O}(\pi )$ denote the number of odd parts in an integer partition $\pi$. In 2005, Stanley introduced a new statistic $\operatorname {srank}(\pi )=\mathcal {O}(\pi )-\mathcal…