• Corpus ID: 125047323

# 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}
}
• Mathematics
• Journal of The London Mathematical Society-second Series
686 Citations
• Mathematics
Philosophical Transactions of the Royal Society A
• 2019
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.
• L. Mutafchiev
• Materials Science
Proceedings of the Steklov Institute of Mathematics
• 2022
Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}
• Mathematics
• 2022
. Let P denote the set of primes and N ⊂ N be a set with arbitrary weights attached to its elements. Set p N ( n ) to be the restricted partition function which counts partitions of n with all its
• Mathematics
• 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
• Mathematics
Annals 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
. 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.
• Materials Science
Results in Mathematics
• 2022
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
• Mathematics
Forum 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
• Mathematics
International 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
• Mathematics
Proceedings 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