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Determinantal Formulas for SEM Expansions of Schubert Polynomials


We show that for any permutation w that avoids a certain set of 13 patterns of length 5 and 6, the Schubert polynomial \({\mathfrak {S}}_w\) can be expressed as the determinant of a matrix of elementary symmetric polynomials in a manner similar to the Jacobi–Trudi identity. For such w, this determinantal formula is equivalent to a (signed) subtraction-free expansion of \(\mathfrak S_w\) in the basis of standard elementary monomials.

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Correspondence to Joseph Johnson.

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The authors were partially supported by a National Science Foundation grant DMS-1700302. R. I. Liu was also partially supported by a National Science Foundation Grant CCF-1900460.

Communicated by Vasu Tewari.

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Hatam, H., Johnson, J., Liu, R.I. et al. Determinantal Formulas for SEM Expansions of Schubert Polynomials. Ann. Comb. (2021).

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