Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

An identity involving counts of binary matrices

Hannes Leeb

Abstract

In the context of generating uniform random contingency tables with pre-specified marginals, the number of (binary) matrices with given row- and column-sums is a well-studied object in the literature. We will denote this number by $N(p,q)$, where $p$ and $q$ are the vectors of row- and column-sums. The existing literature is mainly focused on computing or approximating $N(p,q)$. In this paper, we present two identities for polynomials whose coefficients depend on the $N(p,q)$ and explore some consequences.

An identity involving counts of binary matrices

Abstract

In the context of generating uniform random contingency tables with pre-specified marginals, the number of (binary) matrices with given row- and column-sums is a well-studied object in the literature. We will denote this number by , where and are the vectors of row- and column-sums. The existing literature is mainly focused on computing or approximating . In this paper, we present two identities for polynomials whose coefficients depend on the and explore some consequences.

Paper Structure

This paper contains 4 theorems, 12 equations.

Key Result

Proposition 1

For $q \vdash m$ and $x\in \mathbb R$, we have Moreover, for $x, y\in\mathbb R$, we have

Theorems & Definitions (9)

  • Proposition 1
  • proof
  • Remark
  • Corollary 2
  • proof
  • Corollary 3
  • proof
  • Corollary 4
  • proof