منابع مشابه
An algorithmic Littlewood-Richardson rule
We introduce a Littlewood-Richardson rule based on an algorithmic deformation of skew Young diagrams and present a bijection with the classical rule. The result is a direct combinatorial interpretation and proof of the geometric rule presented by Coskun (2000). We also present a corollary regarding the Specht modules of the intermediate diagrams.
متن کاملA Geometric Littlewood-richardson Rule
We describe an explicit geometric Littlewood-Richardson rule, interpreted as deforming the intersection of two Schubert varieties so that they break into Schubert varieties. There are no restrictions on the base field, and all multiplicities arising are 1; this is important for applications. This rule should be seen as a generalization of Pieri’s rule to arbitrary Schubert classes, by way of ex...
متن کاملRefinements of the Littlewood-Richardson Rule
In the prequel to this paper [5], we showed how results of Mason [11], [12] involving a new combinatorial formula for polynomials that are now known as Demazure atoms (characters of quotients of Demazure modules, called standard bases by Lascoux and Schützenberger [6]) could be used to define a new basis for the ring of quasisymmetric functions we call “Quasisymmetric Schur functions” (QS funct...
متن کاملThe Littlewood-Richardson rule, and related combinatorics
Page 4, §1.3: You claim that ”this representation is not unique in general (although in some cases it is, for instance when the sets of rows and columns meeting D are both initial intervals of N)”. This is not literally correct, since the representation is not unique when D is the empty skew diagram, whereas it is clear that the sets of rows and columns meeting the empty skew diagram are both i...
متن کاملA Littlewood-richardson Rule for Grassmannian Permutations
We give a combinatorial rule for computing intersection numbers on a flag manifold which come from products of Schubert classes pulled back from Grassmannian projections. This rule generalizes the known rule for Grassmannians.
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2010
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-009-0184-1