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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...
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.
Twisted Alexander polynomials of 2-bridge knots
Twisted Alexander polynomials 2-bridge knots Geometric Topology
2012/6/30
We investigate the twisted Alexander polynomial of a 2-bridge knot associated to a Fox coloring. For several families of 2-bridge knots, including but not limited to, torus knots and genus-one knots, ...
On the Kauffman-Vogel and the Murakami-Ohtsuki-Yamada Graph Polynomials
Kauffman polynomial HOMFLY-PT polynomia Geometric Topology
2011/9/21
Abstract: This paper consists of three parts. First, we generalize the Jaeger Formula to express the Kauffman-Vogel graph polynomial as a state sum of the Murakami-Ohtsuki-Yamada graph polynomial.
Poincare duality and degrees of twisted Alexander polynomials
twisted Alexander polynomial Reidemeister torsion duality
2011/9/9
Abstract: We prove duality theorems for twisted Reidemeister torsions and twisted Alexander polynomials generalizing the results of Turaev. As a corollary we determine the parity of the degrees of twi...
Tangle sums and factorization of A-polynomials
Tangle sums factorization of A-polynomials Geometric Topology
2011/9/5
Abstract: We show that there exist infinitely many examples of pairs of knots, K_1 and K_2, that have no epimorphism $\pi_1(S^3\setminus K_1) \to \pi_1(S^3\setminus K_2)$ preserving peripheral structu...
Knot Polynomials: Myths and Reality
Alexander polynomial Jones polynomial Homflypt polynomial Khovanov polynomial Kauffman polynomial factorizabitity primeness
2011/8/31
Abstract: This article provides an overview of relative strengths of polynomial invariants of knots and links, such as the Alexander, Jones, Homflypt, and Kaufman two-variable polynomial, Khovanov hom...
Integral and homothetic indecomposability with applications to irreducibility of polynomials
Absolute irreducibility polytopes integral indecomposability
2010/2/25
Being motivated by some methods for construction of homothetically indecomposable polytopes, we obtain new methods for construction of families of integrally indecomposable polytopes. As a result, we ...