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Improved Inclusion-Exclusion Identities and Inequalities Based on a Particular Class of Abstract Tubes

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Improved Inclusion-Exclusion Identities and Inequalities Based on a Particular Class of Abstract Tubes
2.	Creator	Author's name, affiliation, country	Klaus Dohmen; Humboldt-Universitaet zu Berlin
3.	Subject	Discipline(s)	Mathematics
3.	Subject	Keyword(s)	Inclusion-exclusion, Bonferroni inequalities, sieve formula, abstract tube, abstract simplicial complex, partial order, chain, dynamic programming, graph coloring, chromatic polynomial, broken circuit complex, network reliability.
3.	Subject	Subject classification	05A19, 05A20, 05C15, 60C05, 68M15, 90B12, 90B25.
4.	Description	Abstract	Recently, Naiman and Wynn introduced the concept of an abstract tube in order to obtain improved inclusion-exclusion identities and inequalities that involve much fewer terms than their classical counterparts. In this paper, we introduce a particular class of abstract tubes which plays an important role with respect to chromatic polynomials and network reliability. The inclusion-exclusion identities and inequalities associated with this class simultaneously generalize several well-known results such as Whitney's broken circuit theorem, Shier's expression for the reliability of a network as an alternating sum over chains in a semilattice and Narushima's inclusion-exclusion identity for posets. Moreover, we show that under some restrictive assumptions a polynomial time inclusion-exclusion algorithm can be devised, which generalizes an important result of Provan and Ball on network reliability.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	1999-03-26
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/42
10.	Identifier	Digital Object Identifier	10.1214/EJP.v4-42
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 4
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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