Combinatorial approach to enumeration of doubly stochastic non-negative integer square matrices

Combinatorial approach to enumeration of doubly stochastic non-negative integer square matrices -- Let HR(n, r) be equal to the number of matrices with non-negative integer elements such that all row sums and all column sums are equal to r and all elements with indices from a set A are equal to zero. We investigate the properties of the function HR(H, r) and give a combinatorial interpretation of the obtained results. 1. INTRODUCTION In [1] Kenji Mano investigated the number H(n,r) of different ways to allocate rar objects of ra types with r objects of each type among ra persons such that each person receives r objects. The number #(n,r) may be interpreted as the number of ra ra matrices (a tj ) with non-negative integer elements which satisfy the conditions In all subsequent papers H(n,r) is the number of such matrices. In [2] the following hypothesis (ADG hypothesis) was proposed: for any ra and r where = \ \ and ct depend onraand i only. Representation (1.2) was proved by Stanley [3, 4] and Ehrhart [6]. The literature on the ADG hypothesis and its generalizations is quite extensive, we note only the papers [1-12, 14-18]. In [12] a combinatorial approach to evaluation of H(n,r) was suggested. Let R be http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Discrete Mathematics and Applications de Gruyter

Combinatorial approach to enumeration of doubly stochastic non-negative integer square matrices

Loading next page...
 
/lp/de-gruyter/combinatorial-approach-to-enumeration-of-doubly-stochastic-non-sHx0mH3k2B
Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0924-9265
eISSN
1569-3929
DOI
10.1515/dma.1993.3.6.649
Publisher site
See Article on Publisher Site

Abstract

-- Let HR(n, r) be equal to the number of matrices with non-negative integer elements such that all row sums and all column sums are equal to r and all elements with indices from a set A are equal to zero. We investigate the properties of the function HR(H, r) and give a combinatorial interpretation of the obtained results. 1. INTRODUCTION In [1] Kenji Mano investigated the number H(n,r) of different ways to allocate rar objects of ra types with r objects of each type among ra persons such that each person receives r objects. The number #(n,r) may be interpreted as the number of ra ra matrices (a tj ) with non-negative integer elements which satisfy the conditions In all subsequent papers H(n,r) is the number of such matrices. In [2] the following hypothesis (ADG hypothesis) was proposed: for any ra and r where = \ \ and ct depend onraand i only. Representation (1.2) was proved by Stanley [3, 4] and Ehrhart [6]. The literature on the ADG hypothesis and its generalizations is quite extensive, we note only the papers [1-12, 14-18]. In [12] a combinatorial approach to evaluation of H(n,r) was suggested. Let R be

Journal

Discrete Mathematics and Applicationsde Gruyter

Published: Jan 1, 1993

There are no references for this article.

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create folders to
organize your research

Export folders, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off