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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. ...
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.
The objective of this study was to estimate the genetic parameters of milk protein yields in Iranian Holstein dairy cattle. A total of 1,112,082 test-day milk protein yield records of 167,269 first la...
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...
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...
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 ...
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...
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...
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...
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...
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.

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