منابع مشابه
Ribbon Schur operators
A new combinatorial approach to the ribbon tableaux generating functions and q-Littlewood Richardson coefficients of Lascoux, Leclerc and Thibon [10] is suggested. We define operators which add ribbons to partitions and following Fomin and Greene [4] study non-commutative symmetric functions in these operators. This allows us to give combinatorial interpretations for some (skew) q-Littlewood Ri...
متن کاملPositivity results on ribbon Schur function differences
There is considerable current interest in determining when the difference of two skew Schur functions is Schur positive. While the general solution for ribbon Schur functions seems out of reach at present, we determine necessary and sufficient conditions for multiplicity-free ribbons, i.e. those whose expansion as a linear combination of Schur functions has all coefficients either zero or one. ...
متن کاملSchur Operators and Knuth Correspondences
The paper presents a general combinatorial approach to the Schur functions and their modiications, respective generalized Cauchy identities, and bijective Knuth-type correspondences between matrices and pairs of tableaux. All of these appear whenever one has a pair of graphs with the same vertices such that the linear operators associated with these graphs satisfy a certain type of commutation ...
متن کاملComposition of Transpositions and Equality of Ribbon Schur Q-Functions
We introduce a new operation on skew diagrams called composition of transpositions, and use it and a Jacobi-Trudi style formula to derive equalities on skew Schur Q-functions whose indexing shifted skew diagram is an ordinary skew diagram. When this skew diagram is a ribbon, we conjecture necessary and sufficient conditions for equality of ribbon Schur Q-functions. Moreover, we determine all re...
متن کاملRibbon Operators and Hall-Littlewood Symmetric Functions
Abstract. Given a partition λ = (λ1, λ2, . . . λk), let λ rc = (λ2 − 1, λ3 − 1, . . . λk − 1). It is easily seen that the diagram λ/λ is connected and has no 2 × 2 subdiagrams which we shall refer to as a ribbon. To each ribbon R, we associate a symmetric function operator S. We may define the major index of a ribbon maj(R) to be the major index of any permutation that fits the ribbon. This pap...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2008
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2006.01.016