Bipieri tableaux

نویسنده

  • John M. Campbell
چکیده

We introduce a new class of combinatorial objects, which we call “bipieri tableaux,” which arise in a natural way from the evaluation of products consisting of commutative or noncommutative complete homogeneous symmetric functions and elementary symmetric functions through repeated applications of Pieri rules. We prove using sign-reversing involutions on bipieri tableaux an elegant coproduct formula for noncommutative Schur-hooks and an elegant coproduct formula for elements of the shin basis indexed by a reverse hook composition. We show how signreversing involutions on commutative bipieri tableaux may be used to construct alternative combinatorial proofs of special cases of the classical Littlewood-Richardson rule.

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عنوان ژورنال:
  • Australasian J. Combinatorics

دوره 66  شماره 

صفحات  -

تاریخ انتشار 2016