Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A note on plane partition diamonds

Mircea Cimpoeas, Alexandra Teodor

Abstract

We prove new formulas for $\operatorname{DD}_k(n)$, the number of plane partition diamonds of length $k$ of $n$, and, also, for its polynomial part.

A note on plane partition diamonds

Abstract

We prove new formulas for , the number of plane partition diamonds of length of , and, also, for its polynomial part.
Paper Structure (5 sections, 14 theorems, 58 equations)

This paper contains 5 sections, 14 theorems, 58 equations.

Table of Contents

  1. Introduction
  2. Restricted partition function
  3. Preliminaries
  4. New formulas for the number of plane partition diamonds of length $k$ of $n$.
  5. The polynomial part and Sylvester waves of $\mathcal{D}_k(n)$

Key Result

Proposition 2.1

(Bell bell) $p_{\mathbf a}(n)$ is a quasi-polynomial of degree $r-1$, with the period $D$, i.e. where $d_{\mathbf a,m}(n+D)=d_{\mathbf a,m}(n)$ for $0\leq m\leq k-1$ and $n\geq 0$, and $d_{\mathbf a,k-1}(n)$ is not identically zero.

Theorems & Definitions (24)

  • Proposition 2.1
  • Theorem 2.2
  • Theorem 2.3
  • Proposition 2.4
  • Theorem 2.5
  • Theorem 2.6
  • Proposition 3.1
  • proof
  • Proposition 3.2
  • proof
  • ...and 14 more