查看文章

History and Background Richard P. Stanley is well known for his fundamental and important contributions to combinatorics and its relationship to algebra and geometry, in particular in the theory of simplicial complexes. Two kinds of simplicial complexes play central roles in combinatorics: partitionable complexes and Cohen-Macaulay complexes. Stanley posed a central conjecture relating these two notions: Are all Cohen-Macaulay simplicial complexes partitionable? In a 1982 Inventiones Mathematicae paper [4], Stanley defined what is now called the Stanley depth of a graded module over a graded commutative ring. Stanley depth is a geometric invariant of a module that, by a conjecture of Stanley, relates to an algebraic invariant of the module, called simply the depth. It is shown in [2] that this conjecture implies his conjecture about partitionable Cohen-Macaulay simplicial complexes. Our aim here is to …