• Corpus ID: 125047323

Asymptotic formulae in combinatory analysis

  title={Asymptotic formulae in combinatory analysis},
  author={Gordon H. Hardy and Srinivasa Ramanujan},
  journal={Journal of The London Mathematical Society-second Series},

From partitions to Hodge numbers of Hilbert schemes of surfaces

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.

The Limiting Distribution of the Hook Length of a Randomly Chosen Cell in a Random Young Diagram

  • 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}

Partitions into semiprimes

. 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

Sign changes in statistics for plane partitions

. 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

Asymptotics, Turán Inequalities, and the Distribution of the BG-Rank and 2-Quotient Rank of Partitions

. 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

Inequalities for the overpartition function arising from determinants

. 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.

An Asymptotic Expansion for a Twisted Lambert Series Associated to a Cusp Form and the Möbius Function: Level Aspect

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

Distributions on partitions arising from Hilbert schemes and hook lengths

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

Minimal excludant over partitions into distinct parts

. 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

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