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A recursion formula for \(k\)-Schur functions. (English) Zbl 1207.05213
Summary: The Bernstein operators allow one to build recursively the Schur functions. We present a recursion formula for \(k\)-Schur functions at \(t=1\) based on combinatorial operators that generalize the Bernstein operators. The recursion leads immediately to a combinatorial interpretation for the expansion coefficients of \(k\)-Schur functions at \(t=1\) in terms of homogeneous symmetric functions.
MSC:
05E05 Symmetric functions and generalizations
05E10 Combinatorial aspects of representation theory
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