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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An operator approach to the principle of inclusion and exclusion
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by C. J. Liu PDF
Proc. Amer. Math. Soc. 96 (1986), 528-536 Request permission

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.
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 96 (1986), 528-536
  • MSC: Primary 05A15; Secondary 05C30
  • DOI: https://doi.org/10.1090/S0002-9939-1986-0822454-1
  • MathSciNet review: 822454