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AN INTRODUCTION TO MULTIVARIATE KRAWTCHOUK POLYNOMIALS AND THEIR APPLICATIONS
Multivariate polynomial application
2015/7/7
AN INTRODUCTION TO MULTIVARIATE KRAWTCHOUK POLYNOMIALS AND THEIR APPLICATIONS。
Lower Bounds for the Determinantal Complexity of Explicit Low Degree Polynomials
Computational complexity Arithmetic circuits Determinant versus permanent Elementary symmetric polynomial
2012/12/3
The determinantal complexity of a polynomial f (x1, x2, . . . , xn) is the minimum m such that f = detm(L(x1, x2, . . . , xn)), where L(x1, x2, . . . , xn) is a matrix whose entries are affine forms i...
Sutherland-type Trigonometric Models, Trigonometric Invariants and Multivariate Polynomials. III. $E_8$ case
Sutherland-type Trigonometric Models Trigonometric Invariants Multivariate Polynomials
2011/1/19
It is shown that the E8 trigonometric Olshanetsky-Perelomov Hamiltonian, when written in
terms of the Fundamental Trigonometric Invariants (FTI), is in algebraic form, i.e., has polynomial coefficien...
We study the bifurcation locus $B(f)$ of real polynomials $f: \bR^{2n} \to \bR^2$. We find a semialgebraic approximation of $B(f)$ by using the $\rho$-regularity condition and we compare it to the Sar...
We establish an analogue of the Bochner theorem for first order operators of Dunkl type, that is we classify all such operators having polynomial solutions. Under natural conditions it is seen that th...
Lattice Polynomials, 12312-Avoiding Partial Matchings and Even Trees
Lattice Polynomials Partial Matchings Even Trees
2010/11/22
The lattice polynomials $L_{i,j}(x)$ are introduced by Hough and Shapiro as a weighted count of certain lattice paths from the origin to the point $(i,j)$. In particular, $L_{2n, n}(x)$ reduces to th...
Mask formulas for cograssmannian Kazhdan-Lusztig polynomials
Mask formulas cograssmannian Kazhdan-Lusztig polynomials
2010/11/11
We give two contructions of sets of masks on cograssmannian permutations that can be used in Deodhar's formula for Kazhdan-Lusztig basis elements of the Iwahori-Hecke algebra. The constructions are re...
An 4n-point Interpolation Formula for Certain Polynomials
4n-point Interpolation Formula Certain Polynomials
2010/12/6
By using some techniques of the divided difference operators, we establish an 4n-point interpolation formula. Certain polynomials, such as Jackson’s 8 7 terminating summation formula, are special case...
Infinitely many shape invariant potentials and cubic identities of the Laguerre and Jacobi polynomials
invariant potentials Jacobi polynomials cubic identities
2010/4/8
We provide analytic proofs for the shape invariance of the recently discovered (Odake and Sasaki, Phys. Lett. B679 (2009) 414-417) two families of infinitely many exactly solvable one-dimensional quan...