Séminaire Lotharingien de Combinatoire, 91B.35 (2024), 12 pp.
Spencer Daugherty
Extended Schur Functions and Bases Related by Involutions
Abstract.
The extended Schur and shin functions are Schur-like bases of QSym
and NSym. We define a creation operator and a Jacobi-Trudi rule for
certain shin functions and show that a similar Jacobi-Trudi rule does
not exist for every shin function. We also define the skew extended
Schur functions and relate them to the multiplicative structure of
the shin basis. Then, we introduce two new pairs of dual bases that
result from applying the ρ and ω involutions to the
extended Schur and shin functions. These bases are defined
combinatorially via variations on shin-tableaux much like the
row-strict extended Schur functions.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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