Skip to main content Accessibility help
×
Home
Hostname: page-component-99c86f546-5rzhg Total loading time: 0.193 Render date: 2021-12-05T00:02:17.907Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

Note on the combinatorial formula for nHr

Published online by Cambridge University Press:  09 April 2009

G. Baikunth Nath
Affiliation:
Department of Mathematics, University of Queensland, Australia
P. V. Krishna Iyer
Affiliation:
Department of Mathematics, University of Queensland, Australia
Rights & Permissions[Opens in a new window]

Extract

HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

nHr denotes the number of n × n matrices with non-negative integral entries, with row-sums and column-sums all equal to r. Kenji Mano [3] investigated the number nHr in which n distinct objects each replicated r times can be distributed in equal numbers among n cells. He gives an intricate formula for the case r = 2. Recently, Anand et al. [1], making use of partitions, extended it to 3Hr and stated a plausible formula for nHr.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Anand, H., Dumir, V. C. and Gupta, H., ‘A Combinatorial Distribution Problem’, Duke Math. J. 33 (1966), 757769.CrossRefGoogle Scholar
[2]David, F. N., and Kendall, M. G., ‘Tables of Symmetric Functions: Part IV’, Biometrika 40 (1953), 427446.CrossRefGoogle Scholar
[3]Mano, Kenji, ‘On the formula of nHr’, Scientific Reports of the Faculty of Literature and Science: Hirosaki University 8 (1961), 5860.Google Scholar
You have Access
3
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Note on the combinatorial formula for nHr
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Note on the combinatorial formula for nHr
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Note on the combinatorial formula for nHr
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *