2002/01/18 by Raul Cordovil, Cordovil, Raul, David Forge +1
Mathematics · #05B35 #14F40 #52C35 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AT #math.CO #msc:05B35 #msc:14F40 #msc:52C35
paper · pdf · doi:10.48550/arxiv.math/0201174
9 pages, Latex to appear in "Annals of Combinatorics"
openalex publication_date 2002/01/18 · arxiv created 2003/07/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.