Related papers: The cyclotomic polynomial topologically

The notion of block divisibility naturally leads one to introduce unitary cyclotomic polynomials. We formulate some basic properties of unitary cyclotomic polynomials and study how they are connected with cyclotomic, inclusion-exclusion and…

In this paper, we list several interesting structures of cyclotomic polynomials: specifically relations among blocks obtained by suitable partition of cyclotomic polynomials. We present explicit and self-contained proof for all of them,…

We give explicit upper bounds for coefficients of polynomials appearing in Gauss-Kra\"{i}tchik formula for cyclotomic polynomials. We use a certain relation between elementary symmetric polynomials and power sums polynomials.

We establish necessary and sufficient conditions for a polynomial to be divisible by a cyclotomic polynomials and derive new formulas involving Ramanujan sums as an application of our results. Additionally, we provide new insights into the…

Symmetric edge polytopes are a recent and well-studied family of centrally symmetric polytopes arising from graphs. In this paper, we introduce a generalization of this family to arbitrary simplicial complexes. We show how topological…

We discuss various aspects of representation of a polynomial as a sum of monomials (for example, uniqueness of such representation and related estimations).

Using the cyclotomic identity we compute sums over d-tuples of monic polynomials in F_q[x] weighted by the multiplicity of their irreducible factors. As consequences we determine explicit expressions for the number of d-tuples of…

This paper investigates coefficients of cyclotomic polynomials theoretically and experimentally. We prove the following result. {{\em If $n=p_1\ldots p_k$ where $p_i$ are odd primes and $p_1<p_2<\ldots<p_r<p_1+p_2<p_{r+1}<\ldots<p_t$ with…

This article investigates the homotopy theory of simplicial commutative algebras with a view to homological applications.

We determine the symmetrized topological complexity of the circle, using primarily just general topology.

Cyclotomic polynomials are basic objects in Number Theory. Their properties depend on the number of distinct primes that intervene in the factorization of their order, and the binary case is thus the first nontrivial case. This paper sees…

Let $\Psi_n(x)$ be the monic polynomial having precisely all non-primitive $n$th roots of unity as its simple zeros. One has $\Psi_n(x)=(x^n-1)/\Phi_n(x)$, with $\Phi_n(x)$ the $n$th cyclotomic polynomial. The coefficients of $\Psi_n(x)$…

Some years ago, the harmonic polynomial was introduced in order to understand better the harmonic topological index; for instance, it allows to obtain bounds of the harmonic index of the main products of graphs. Here, we obtain several…

We consider binomial and inverse binomial sums at infinity and rewrite them in terms of a small set of constants, such as powers of $\pi$ or $\log(2)$. In order to perform these simplifications, we view the series as specializations of…

We consider here a particular quadratic equation linking two elements of a C-Algebra. By analysing powers of the unknowns, it appears a double sequence of polynomials related to classical Bernoulli polynomials. We get the generating…

We study a simplicial mixed polynomial of cyclic type and its associated weighted homogeneous polynomial. In the present paper, we show that their links are diffeomorphic and their Milnor fibrations are isomorphic.

In this work we deal with a symbolic approach to the general quadratic polynomial decomposition. By means of a symbolic implementation, we investigate some properties of the components sequences like orthogonality and symmetry. We present…

We describe a congruence property of solvable polynomials over Q, based on the irreducibility of cyclotomic polynomials over number fields that meet certain conditions.

We use a combinatorial interpretation of the coefficients of zonal Kerov polynomials as a number of unoriented maps to derive an explicit formula for the coefficients in genus one.

We classify two-variable polynomials which are rational of simple type. These are precisely the two-variable polynomials with trivial homological monodromy.