. C O ] 2 3 M ay 2 00 7 COINCIDENCES AMONG SKEW SCHUR FUNCTIONS
نویسندگان
چکیده
New sufficient conditions and necessary conditions are developed for two skew diagrams to give rise to the same skew Schur function. The sufficient conditions come from a variety of new operations related to ribbons (also known as border strips or rim hooks). The necessary conditions relate to the extent of overlap among the rows or among the columns of the skew diagram.
منابع مشابه
ar X iv : m at h / 05 05 27 3 v 1 [ m at h . C O ] 1 2 M ay 2 00 5 CELL TRANSFER AND MONOMIAL POSITIVITY
We give combinatorial proofs that certain families of differences of products of Schur functions are monomial-positive. We show in addition that such monomial-positivity is to be expected of a large class of generating functions with combinatorial definitions similar to Schur functions. These generating functions are defined on posets with labelled Hasse diagrams and include for example generat...
متن کاملCoincidences among Skew Schur Functions
New sufficient conditions and necessary conditions are developed for two skew diagrams to give rise to the same skew Schur function. The sufficient conditions come from a variety of new operations related to ribbons (also known as border strips or rim hooks). The necessary conditions relate to the extent of overlap among the rows or among the columns of the skew diagram.
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We introduce and study a new basis in the algebra of symmetric functions. The elements of this basis are called the Frobenius–Schur functions (FSfunctions, for short). Our main motivation for studying the FS-functions is the fact that they enter a formula expressing the combinatorial dimension of a skew Young diagram in terms of the Frobenius coordinates. This formula plays a key role in the as...
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We define an equivalence relation on integer compositions and show that two ribbon Schur functions are identical if and only if their defining compositions are equivalent in this sense. This equivalence is completely determined by means of a factorization for compositions: equivalent compositions have factorizations that differ only by reversing some of the terms. As an application, we can deri...
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