Geodesic
Flagged Schur polynomial duality via a lattice path bijection
Eoghan McDowell1
1Okinawa Institute of Science and Technology
The electronic journal of combinatorics, Tome 30 (2023) no. 1
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This paper proves an identity between flagged Schur polynomials, giving a duality between row flags and column flags. This identity generalises both the binomial determinant duality theorem due to Gessel and Viennot and the symmetric function duality theorem due to Aitken. As corollaries we obtain the lifts of the binomial determinant duality theorem to \(q\)-binomial coefficients and to symmetric polynomials. Our method is a path counting argument on a novel lattice generalising that used by Gessel and Viennot.
DOI : 10.37236/11200
Classification : 05A10, 05A19, 05E05, 05A17
Mots-clés : skew Schur polynomials, binomial duality theorem

Eoghan McDowell  1

1 Okinawa Institute of Science and Technology 
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Eoghan McDowell. Flagged Schur polynomial duality via a lattice path bijection. The electronic journal of combinatorics, Tome 30 (2023) no. 1. doi: 10.37236/11200

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