Codes and shifted codes
J. T. Hird, Naihuan Jing, Ernest Stitzinger
TL;DR
This paper introduces a new combinatorial model of extended codes that unifies the action of Bernstein operators on Schur and Schur Q-functions, providing a natural algebraic framework for functions indexed by compositions.
Contribution
It develops a novel combinatorial model of extended codes that generalizes previous results and offers a natural algebraic setting for Schur functions indexed by compositions.
Findings
Unified combinatorial relation for codes
Extension of Bernstein operator actions
New algebraic structure for Schur functions
Abstract
The action of the Bernstein operators on Schur functions was given in terms of codes in [CG] and extended to the analog in Schur Q-functions in [HJS]. We define a new combinatorial model of extended codes and show that both of these results follow from a natural combinatorial relation induced on codes. The new algebraic structure provides a natural setting for Schur functions indexed by compositions.
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