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Diagonal Bases in Orlik-Solomon Type Algebras
Raul Cordovil1 and David Forge2
1Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal
cordovil@math.ist.utl.pt
2Laboratoire de Recherche en Informatique, Bâtiment 490, Université Paris Sud 91405 Orsay Cedex, France
forge@lri.fr
Annals of Combinatorics 7 (3) p.247-257 September, 2003
AMS Subject Classification: 52C35, 05B35, 14F40
Abstract:
To encode an important property of the "no broken circuit bases" of the Orlik-Solomon-Terao algebras, Szenes has introduced a particular type of bases, the so called "diagonal basis." We prove that this definition extends naturally to a large class of algebras, the so called -algebras. Our definitions make also use of an "iterative residue formula" based on the matroidal operation of contraction. This formula can be seen as the combinatorial analogue of an iterative residue formula introduced by Szenes. As an application we deduce nice formulas to express a pure element in a diagonal basis.
Keywords: arrangement of hyperplanes, broken circuit, cohomology algebra, matroid, Orlik-Solomon algebra

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