Generalized Eulerian Numbers and the Topology of the Hessenberg Variety of a Matrix.

dc.contributor.author	Mari, Filippo de	en_US
dc.contributor.author	Shayman, M.A.	en_US
dc.contributor.department	ISR	en_US
dc.date.accessioned	2007-05-23T09:39:11Z
dc.date.available	2007-05-23T09:39:11Z
dc.date.issued	1987	en_US
dc.description.abstract	Let A {AN ELEMENT OF} gl(n,C) and let p be a positive integer. The Hessenberg variety of degree p for A is the subvariety Hess (p, A) of the complete flag manifold consisting of those flags S_1, {SUBSET}... {SUBSET} S_{n-1}in C^n which satisfy the condition AS_i {SUBSET} S_{i+p} for all i. We show that if A has distinct eigenvalues, then Hess (p, A) is smooth and connected. The odd Betti numbers of Hess (p, A) vanish, while the even Betti numbers are given by a natural generalization of the Eulerian numbers.	en_US
dc.format.extent	881959 bytes
dc.format.mimetype	application/pdf
dc.identifier.uri	http://hdl.handle.net/1903/4678
dc.language.iso	en_US	en_US
dc.relation.ispartofseries	ISR; TR 1987-173	en_US
dc.title	Generalized Eulerian Numbers and the Topology of the Hessenberg Variety of a Matrix.	en_US
dc.type	Technical Report	en_US

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