Integer partitions, probabilities and quantum modular forms

DOI10.1186/s40687-017-0102-4zbMath1371.05021OpenAlexW2607770616WikidataQ59611934 ScholiaQ59611934MaRDI QIDQ2408989

Robert C. Rhoades, Hieu T. Ngo

Publication date: 10 October 2017

Published in: Research in the Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s40687-017-0102-4

zbMATH Keywords

random integer partition

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Combinatorial probability (60C05) Elementary theory of partitions (11P81) Asymptotic enumeration (05A16) Analytic theory of partitions (11P82) Partition identities; identities of Rogers-Ramanujan type (11P84)

Related Items

Statistics for unimodal sequences, Torus knots and quantum modular forms, The number of parts in certain residue classes of integer partitions, ``Strange combinatorial quantum modular forms, Congruences for Taylor expansions of quantum modular forms, On the number of parts in congruence classes for partitions into distinct parts, Rademacher expansions and the spectrum of 2d CFT, Distributions on partitions arising from Hilbert schemes and hook lengths, On the number of parts of integer partitions lying in given residue classes, Asymptotics, Turán inequalities, and the distribution of the BG-rank and 2-quotient rank of partitions, Limit laws for rational continued fractions and value distribution of quantum modular forms, Hook length biases and general linear partition inequalities, A note on the equidistribution of 3-colour partitions, On a Tauberian theorem of Ingham and Euler-Maclaurin summation, Asymptotic equidistribution for partition statistics and topological invariants, Unexpected biases between congruence classes for parts in \(k\)-indivisible partitions, Graph schemes, graph series, and modularity, Statistical structure of concave compositions, Asymptotic formulae for mixed congruence stacks, On weighted overpartitions related to some q-series in Ramanujan’s lost notebook

Uses Software

• DLMF

Cites Work

• Negative index Jacobi forms and quantum modular forms
• Asymptotics for \(q\)-expansions involving partial theta functions
• Concave compositions
• Limit distributions of smallest gap and largest repeated part in integer partitions
• Asymptotics for the number of row-Fishburn matrices
• Weighted forms of Euler's theorem
• Analysis of some new partition statistics
• Dyson's ranks and Maass forms
• Successions in integer partitions
• On the distribution of the longest run in number partitions
• Asymptotics of maximal and typical dimensions of irreducible representations of a symmetric group
• Ramanujan's lost notebook. V: Euler's partition identity
• Partitions and indefinite quadratic forms.
• q-identities for Maass waveforms
• The expected number of parts in a partition of n
• On a likely shape of the random Ferrers diagram
• Modular forms and quantum invariants of \(3\)-manifolds
• Confirming two conjectures about the integer partitions
• \(q\)-series identities and values of certain \(L\)-functions
• Combinatorial proofs of \(q\)-series identities
• Period functions and cotangent sums
• Concave and convex compositions
• Modularity of the concave composition generating function
• On the number of even and odd strings along the overpartitions of \(n\)
• The \(f(q)\) mock theta function conjecture and partition ranks
• On some problems of a statistical group theory. V
• On some problems of a statistical group theory. VII
• Extension of Abel's Lemma with \(q\)-series implications
• The distribution of the number of summands in the partitions of a positive integer
• On Dyson’s crank conjecture and the uniform asymptotic behavior of certain inverse theta functions
• On Dyson’s crank distribution conjecture and its generalizations
• Improved bounds on metastability thresholds and probabilities for generalized bootstrap percolation
• Euler’s constant: Euler’s work and modern developments
• MOCK THETA FUNCTIONS AND QUANTUM MODULAR FORMS
• K-RUN OVERPARTITIONS AND MOCK THETA FUNCTIONS
• Taylor coefficients of mock-Jacobi forms and moments of partition statistics
• A General Asymptotic Scheme for the Analysis of Partition Statistics
• An extension of the Hardy-Ramanujan circle method and applications to partitions without sequences
• The number of smallest parts in the partitions of n
• New Combinatorial Interpretations of Ramanujan's Partition Congruences Mod 5,7 and 11
• Dyson’s crank of a partition
• The Structure of Random Partitions of Large Integers
• On the derivatives of the Bessel and Struve functions with respect to the order
• Families of quasimodular forms and Jacobi forms: The crank statistic for partitions
• Self-conjugate vector partitions and the parity of the spt-function
• Note on a partition limit theorem for rank and crank
• Asymptotics for the Number of Strongly Unimodal Sequences
• Asymptotic formulae for partition ranks
• Convolution Bootstrap Percolation Models, Markov-type Stochastic Processes, and Mock Theta Functions
• On asymptotic formulas for certain $q$-series involving partial theta functions
• A PROOF OF ANDREWS’ CONJECTURE ON PARTITIONS WITH NO SHORT SEQUENCES
• Asymptotic inequalities for positive crank and rank moments
• Partitions
• The rank of a unimodal sequence and a partial theta identity of Ramanujan
• On some problems of a statistical group-theory. II
• STACKS (II)
• On some problems of a statistical group-theory. III
• On some problems of a statistical group-theory. IV
• A Convergent Series for the Partition Function p ( n )
• Period functions for Maass wave forms. I.
• Vassiliev invariants and a strange identity related to the Dedekind eta-function
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item