Flagged Hamel--Goulden formulas
Alibek Adilzhan, Damir Yeliussizov
TL;DR
This paper introduces new determinantal formulas for flagged supersymmetric Schur functions and related symmetric functions, extending classical results and providing tools for further algebraic combinatorics research.
Contribution
It generalizes existing formulas to flagged and supersymmetric cases, deriving new determinantal representations for various symmetric functions.
Findings
Derived new determinantal formulas for flagged supersymmetric Schur functions
Extended classical Jacobi--Trudi and Giambelli formulas to flagged cases
Provided formulas for dual refined canonical stable Grothendieck polynomials
Abstract
We obtain Hamel--Goulden-type ribbon decomposition determinantal formulas for flagged supersymmetric Schur functions. As an application, we derive corresponding new determinantal formulas dual refined canonical stable Grothendieck polynomials. These results generalize and produce a number of new determinantal formulas for these symmetric functions including Jacobi--Trudi and skew Giambelli-type determinants.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Mathematical functions and polynomials