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A Counting Lemma and Multiple Combinatorial Stokes' Theorem

✍ Scribed by Shyh-Nan Lee; Mau-Hsiang Shih


Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
150 KB
Volume
19
Category
Article
ISSN
0195-6698

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✦ Synopsis


We prove in the present paper a counting lemma for bipartite digraphs which is useful in the combinatorics of pseudomanifolds. By an application of the lemma, we prove a multiple combinatorial Stokes' theorem, generalizing the 1967 Ky Fan combinatorial formula to multiple labelings.


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We prove a new vertex-splitting lemma which states that if a multigraph G has maximum multiplicity of at most p, then each vertex u can be split into W(d(u)Γ‚p)X new vertices, w(d(u)Γ‚p)x of degree p, with the multiple edges being shared out between the new vertices in such a way that each multiple ed