Diagonal bases in Orlik-Solomon type algebras

Details Diagonal bases in Orlik-Solomon type algebras Diagonal bases in Orlik-Solomon type algebras

2002-01-18

arxiv.org/abs/math/0201174v2

Mathematics

Combinatorics

9 pages, Latex to appear in "Annals of Combinatorics"

Scientific paper

To encode an important property of the "no broken circuit bases" of the Orlik-Solomon-Terao algebras, Andras 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 chi-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.

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