Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


An operator approach to the principle of inclusion and exclusion

Author: C. J. Liu
Journal: Proc. Amer. Math. Soc. 96 (1986), 528-536
MSC: Primary 05A15; Secondary 05C30
MathSciNet review: 822454
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Using an operator approach we derive Sylvester-Whitworth formulae for sets $ A$'s. By the same token we treat the problem where both sets of $ A$'s and $ B$'s are involved. Our result extends the Sylvester-Whitworth inclusion and exclusion formula to the resolution of the number of elements in exactly $ {m_1}$ sets of $ A$'s and $ {m_2}$ sets of $ B$'s respectively. The formula are applied to the complete graph and complete bipartite graph. The enumeration of spanning subgraphs with any preassigned number of disconnected cycles is solved, together with the case where any preassigned number of vertices have degree one.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 05A15, 05C30

Retrieve articles in all journals with MSC: 05A15, 05C30

Additional Information

PII: S 0002-9939(1986)0822454-1
Article copyright: © Copyright 1986 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia