Related Experiment Video
Updated: Jul 1, 2026

Self-assembly of Complex Two-dimensional Shapes from Single-stranded DNA Tiles
Published on: May 8, 2015
Partitions with short sequences and mock theta functions
1Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA. andrews@math.psu.edu
Abstract:
P. A. MacMahon was the first to examine integer partitions in which consecutive integers were not allowed as parts. Such partitions may be described as having sequences of length 1. Recently it was shown that partitions containing no sequences of consecutive integers of length k are of interest in seemingly unrelated problems concerning threshold growth models. The object now is to develop the subject intrinsically to both provide deeper understanding of the theory and application of partitions and reveal the surprising role of Ramanujan's mock theta functions.
Related Concept Videos
Extraction: Partition and Distribution Coefficients
For extracting a solute from an aqueous phase into an organic...
Thermal Sigmatropic Reactions: Overview
Sigmatropic shifts are classified based on an order term [i, j ], where i and j indicate the number of atoms across which each end of the σ bond migrates. Below are examples of a [3,3] sigmatropic shift in 1,5-hexadiene, referred to as...
Determination of Pi Terms
The theorem indicates that the number...
Long Division of Polynomials
Synthetic Disvision of Polynomials
Rationalizing Substitutions

