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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Fast Numerical Evaluation of Generalized Todd Polynomials
广义托德多项式 的快速数值 评估
2023/4/23
Fast Numerical Evaluation of Generalized Todd Polynomials.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Zeros of complete symmetric polynomials over finite fields
有限域 完全对称 多项式 零点
2023/4/13
Wan and Zhang have recently obtained a nontrivial lower bound for the number of zeros of complete symmetric polynomials over finite fields, and proposed a problem whether their bound can be improved. ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Local Method for Compositional Inverses of Permutation Polynomials
置换 多项式复合逆 局部方法
2023/4/18
In this talk, we will talk about a local method to find compositional inverses of all PPs, some new PPs and their compositional inverses are given.
We use the Pieri and Giambelli formulas of [BKT1, BKT3] and
the calculus of raising operators developed in [BKT2, T1] to prove a tableau
formula for the eta polynomials of [BKT3] and the Stanley sym...
DOUBLE THETA POLYNOMIALS AND EQUIVARIANT GIAMBELLI FORMULAS
EQUIVARIANT GIAMBELLI FORMULAS DOUBLE THETA POLYNOMIALS
2015/12/17
We use Young’s raising operators to introduce and study double
theta polynomials, which specialize to both the theta polynomials of Buch,
Kresch, and Tamvakis, and to double (or factorial) Schur S-p...
DOUBLE ETA POLYNOMIALS AND EQUIVARIANT GIAMBELLI FORMULAS
DOUBLE ETA POLYNOMIALS EQUIVARIANT GIAMBELLI FORMULAS
2015/12/17
We use Young’s raising operators to introduce and study double
eta polynomials, which are an even orthogonal analogue of Wilson’s double
theta polynomials. Our double eta polynomials give Giambelli ...
STANDARD CONJECTURES FOR THE ARITHMETIC GRASSMANNIAN G(2; N) AND RACAH POLYNOMIALS
STANDARD CONJECTURES RACAH POLYNOMIALS
2015/12/17
We prove the arithmetic Hodge index and hard Lefschetz conjectures for the Grassmannian G = G(2; N) parametrizing
lines in projective space, for the natural arithmetic Lefschetz operator de ned via t...
DOUBLE SCHUBERT POLYNOMIALS AND DEGENERACY LOCI FOR THE CLASSICAL GROUPS
DOUBLE SCHUBERT POLYNOMIALS DEGENERACY LOCI
2015/12/17
We propose a theory of double Schubert polynomials Pw(X;Y )
for the Lie types B, C, D which naturally extends the family of Lascoux and
Schutzen Ä berger in type A. These polynomials satisfy po...
Fulton's universal Schubert polynomials [F3] represent degeneracy loci for morphisms of vector bundles with rank conditions coming from a
permutation.
Fulton's universal Schubert polynomials give cohomology formulas
for a class of degeneracy loci, which generalize Schubert varieties. The Ktheoretic quiver formula of Buch expresses the structure she...
STABLE GROTHENDIECK POLYNOMIALS AND K-THEORETIC FACTOR SEQUENCES
STABLE GROTHENDIECK POLYNOMIALS K-THEORETIC FACTOR
2015/12/17
We formulate a nonrecursive combinatorial rule for the expansion
of the stable Grothendieck polynomials of [Fomin-Kirillov '94] in the basis of
stable Grothendieck polynomials for partitions. This g...
SCHUBERT POLYNOMIALS AND ARAKELOV THEORY OF SYMPLECTIC FLAG VARIETIES
SCHUBERT POLYNOMIALS ARAKELOV THEORY
2015/12/17
Let X = Sp2n/B the flag variety of the symplectic group. We
propose a theory of combinatorially explicit Schubert polynomials which represent the Schubert classes in the Borel presentation of t...
SCHUBERT POLYNOMIALS AND ARAKELOV THEORY OF ORTHOGONAL FLAG VARIETIES
SCHUBERT POLYNOMIALS ARAKELOV THEORY
2015/12/17
We propose a theory of combinatorially explicit Schubert polynomials which represent the Schubert classes in the Borel presentation of the
cohomology ring of the orthogonal flag variety X = SON...
We use Young’s raising operators to give short and uniform proofs
of several well known results about Schur polynomials and symmetric functions, starting from the Jacobi-Trudi identity.
ORTHOGONAL POLYNOMIALS ON THE SIERPINSKI GASKET
Jacobi matrix Laplacian Sierpinski Gasket Orthogonal Polynomials Recursion Relation
2015/12/10
The construction of a Laplacian on a class of fractals which includes the Sierpinski gasket (SG) has given rise to an intensive research on analysis on fractals. For instance, a complete theory of pol...