Results 81 to 90 of about 18,601 (168)
Schubert Polynomial Analogues for Degenerate Involutions [PDF]
We survey the recent study of involution Schubert polynomials and a modest generalization that we call degenerate involution Schubert polynomials. We cite several conditions when (degenerate) involution Schubert polynomials have simple factorization formulae.
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Cauchy Identities for Universal Schubert Polynomials
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Generation of Schubert polynomial series via nanometre-scale photoisomerization in photochromic single crystal and double-probe optical near-field measurements. [PDF]
Uchiyama K +6 more
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Noncommutative Schubert Calculus and Grothendieck Polynomials
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Order recognition by Schubert polynomials generated by optical near-field statistics via nanometre-scale photochromism. [PDF]
Uchiyama K +8 more
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On the Multiplication of Schubert Polynomials
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QUANTUM SCHUBERT POLYNOMIALS AND QUANTUM SCHUR FUNCTIONS
We introduce the quantum multi–Schur functions, quantum factorial Schur functions and quantum Macdonald polynomials. We prove that for restricted vexillary permutations, the quantum double Schubert polynomial coincides with some quantum multi-Schur function and prove a quantum analog of the Nägelsbach–Kostka and Jacobi–Trudi formulae for the quantum ...
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Surrogates for Liquid-Liquid Extraction. [PDF]
Neubauer M +4 more
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