Results 31 to 40 of about 18,601 (168)
Proceedings of the American Mathematical Society, 2003 We define skew Schubert polynomials to be normal form (polynomial) representatives of certain classes in the cohomology of a flag manifold. We show that this definition extends a recent construction of Schubert polynomials due to Bergeron and Sottile in terms of certain increasing labeled chains in Bruhat order of the symmetric group.
Lenart, Cristian, Sottile, Frank
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Balanced Labellings and Schubert Polynomials
European Journal of Combinatorics, 1997 By a diagram the authors mean a finite collection of cells in \({\mathbb Z}\times {\mathbb Z}\). They consider balanced labellings of diagrams. Special cases of these objects are the standard Young tableaux and the balanced tableaux introduced by \textit{P. Edelman} and \textit{C. Greene} [Adv. Math. 63, 42-99 (1987; Zbl 0616.05005)]. It turns out that
Fomin, Sergey +3 more
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Forum of Mathematics, SigmaSchubert polynomials are polynomial representatives of Schubert classes in the cohomology of the complete flag variety and have a combinatorial formulation in terms of bumpless pipe dreams.
Tuong Le +4 more
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A Pieri-type formula for isotropic flag manifolds
, 1998 We give the formula for multiplying a Schubert class on an odd orthogonal or symplectic flag manifold by a special Schubert class pulled back from a Grassmannian of maximal isotropic subspaces.
Bergeron, Nantel, Sottile, Frank
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Wonderful symmetric varieties and Schubert polynomials
Ars Mathematica Contemporanea, 2018 19 ...
Can, Mahir Bilen +2 more
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Vanishing of Schubert coefficients via the effective Hilbert nullstellensatz
Forum of Mathematics, SigmaSchubert Vanishing is a problem of deciding whether Schubert coefficients are zero. Until this work it was open whether this problem is in the polynomial hierarchy ${{\mathsf {PH}}}$ .
Igor Pak, Colleen Robichaux
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Antenna Array Design in MIMO Radar Using NSK Polynomial Factorization Algorithm
International Journal of Antennas and Propagation, 2016 The work presented here is concerned with the antenna array design in collocated multiple-input multiple-output (MIMO) radars. After knowing the system requirements, the antenna array design problem is formulated as a standard polynomial factorization ...
Shuainan Gu +3 more
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Sparse multivariate polynomial interpolation in the basis of Schubert polynomials
, 2016 Schubert polynomials were discovered by A. Lascoux and M. Sch\"utzenberger in the study of cohomology rings of flag manifolds in 1980's. These polynomials generalize Schur polynomials, and form a linear basis of multivariate polynomials.
Mukhopadhyay, Priyanka, Qiao, Youming
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Some Combinatorial Properties of Schubert Polynomials [PDF]
Journal of Algebraic Combinatorics, 1993 The main result of the Section 1 of the reviewed paper is to give an explicit combinatorial interpretation of the Schubert polynomial \({\mathfrak S}_ w\) in terms of the reduced decompositions of the permutation \(w\). This interpretation is completely different from an earlier conjecture of A. Kohnert and a theorem of N. Bergeron (see \textit{I.
Billey, Sara C. +2 more
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Skew Schubert functions and the Pieri formula for flag manifolds
, 1997 We show the equivalence of the Pieri formula for flag manifolds and certain identities among the structure constants, giving new proofs of both the Pieri formula and of these identities.
Bergeron, Nantel, Sottile, Frank
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