Related papers: The cyclotomic polynomial topologically
The purpose of this paper is to study the topology of certain toric varieties $X_I$, arising as quotients of the action of $\C^*$ on complements of arrangements of coordinate subspaces in $\C^n$, and to improve the homotopy stability…
We present a more general proof that cyclotomic polynomials are irreducible over Q and other number fields that meet certain conditions. The proof provides a new perspective that ties together well-known results, as well as some new…
We explain a method for calculating the cohomology of line bundles on a toric variety in terms of the cohomology of certain constructible sheaves on the polytope. We show its effective use by means of some examples.
In this paper, we give a description of the cohomology groups of the symmetric powers of the tautological bundle associated with a sufficiently positive line bundle on the Hilbert scheme of 2 or 3 points on a smooth projective complex…
For any orbifold M, we explicitly construct a simplicial complex S(M) from a given triangulation of the `coarse' underlying space together with the local isotropy groups of M. We prove that, for any local system on M, this complex S(M) has…
We classify homogeneous polynomials which split as powers of linear forms and whose polar map is birational.
We introduce an object that has obvious similarity to the classical one - the algebra of supersymmetric polynomials. Despite the similarity, the known structure theorems on supersymmetric polynomials do not help in the study of the new…
In this paper, we gave some properties of binomial coefficient.
In this paper one extends the binomial and trinomial coefficients to the concept of 'k-nomial' coefficients, and one obtains some properties of these. As an application one generalizes Pascal's triangle.
We apply a symbolic approach of the general quadratic decomposition of polynomial sequences - presented in a previous article referenced herein - to polynomial sequences fulfilling specific orthogonal conditions towards two given…
We describe a method to evaluate multivariate polynomials over a finite field and discuss its multiplicative complexity.
This paper can be considered as an extension to our paper [On symplectically harmonic forms on six-dimensional nilmanifolds, Comment. Math. Helv. 76 (2001), n 1, 89-109]. Also, it contains a brief survey of recent results on symplectically…
In this paper, the discriminant of homogeneous polynomials is studied in two particular cases: a single homogeneous polynomial and a collection of n-1 homogeneous polynomials in n variables. In these two cases, the discriminant is defined…
We define the concept of symplectic foliation on a symplectic manifold and provide a method of constructing many examples, by using asymptotically holomorphic techniques.
We apply tropical geometry to study the image of a map defined by Laurent polynomials with generic coefficients. If this image is a hypersurface then our approach gives a construction of its Newton polytope.
This paper presents a closed form polynomial expression for the binary cyclotomic polynomial. We contrast this against expressions for binary cyclotomic polynomials in (Lam and Leung 1996) and (Lenstra 1979).
Explicit generators are given for the ring of invariant polynomials under the coadjoint representation of certain inhomogeneous groups.
Article explicitly expresses Subgraph Isomorphism by a polynomial size asymmetric linear system.
We provide simple criteria and algorithms for expressing homogeneous polynomials as sums of powers of independent linear forms, or equivalently, for decomposing symmetric tensors into sums of rank-1 symmetric tensors of linearly independent…
We give an explicit formula for the Hankel transform of a regular sequence in terms of the coefficients of the associated orthogonal polynomials and the sequence itself. We apply this formula to some sequences of combinatorial interest,…