Related papers: Some Interesting Integer Polynomial Maps
We describe birational representations of discrete groups generated by involutions, having their origin in the theory of exactly solvable vertex-models in lattice statistical mechanics. These involutions correspond respectively to two kinds…
We describe a wide class of polynomials, which is a natural generalization of Hurwitz stable polynomials. We also give a detailed account of so-called self-interlacing polynomials, which are dual to Hurwitz stable polynomials but have only…
We present an algorithm to find invariant poynomial transformations of integer sequences, using the classical invariant theory approach.
In this paper, with the help of trinomial coefficients we study some arithmetic properties of certain determiants involving reciprocals of binary quadratic forms over finite fields.
We provide new examples of integrable rational maps in four dimensions with two rational invariants, which have unexpected geometric properties, as for example orbits confined to non algebraic varieties, and fall outside classes studied by…
We prove some properties of analytic multiplicative and sub-multiplicative cocycles. The results allow to construct natural invariant analytic sets associated to complex dynamical systems.
We investigate algebraic and arithmetic properties of a class of sequences of sparse polynomials that have binomial coefficients both as exponents and as coefficients. In addition to divisibility and irreducibility results we also consider…
New exceptional (i.e. non-repeating) prime number multiplets are given and formulated in terms of arithmetic progressions, along with laws governing them. Accompanying repeating prime number multiplets are pointed out. Prime number…
In this paper, we obtain a general expression for the entries of the r. (r is integer) power of a certain n-square complex tridiagonal matrix. In addition, we get the complex factorizations of Fibonacci polynomials, Fibonacci and Pell…
We classify the simple modules of the exceptional algebraic supergroups over an algebraically closed field of prime characteristic.
For $x\ge0$ let $\pi(x)$ be the number of primes not exceeding $x$. The asymptotic behaviors of the prime-counting function $\pi(x)$ and the $n$-th prime $p_n$ have been studied intensively in analytic number theory. Surprisingly, we find…
We consider the dynamics of holomorphic polynomials in $\mathbb C$. We show that the ergodic properties of the map can be seen already from the real parts of the orbits.
The subject matter of this work is quadratic and cubic polynomial functions with integer coefficients;and all of whose roots are integers. The material of this work is directed primarily at educators,students,and teachers of…
The Schinzel Hypothesis is a celebrated conjecture in number theory linking polynomial values and prime numbers. In the same vein we investigate the common divisors of values $P_1(n),\ldots, P_s(n)$ of several polynomials. We deduce this…
We introduce new polynomial invariants of a finite-dimensional semisimple and cosemisimple Hopf algebra A over a field by using the braiding structures of A. We investigate basic properties of the polynomial invariants including stability…
Some important properties of the chromatic polynomial also hold for any polynomial set map satisfying p_S(x+y)=\sum_{T\uplus U=S}p_T(x)p_U(y). Using umbral calculus, we give a formula for the expansion of such a set map in terms of any…
We present a moduli space for similar triangles, then classify triangle maps $f$ that arise from linear maps on this space, with the well-studied pedal map as a special case. Each linear triangle map admits a Markov partition, showing that…
In this paper we study some structure properties of primitive weird numbers in terms of their factorization. We give sufficient conditions to ensure that a positive integer is weird. Two algorithms for generating weird numbers having a…
This article starts a computational study of congruences of modular forms and modular Galois representations modulo prime powers. Algorithms are described that compute the maximum integer modulo which two monic coprime integral polynomials…
We explore some interesting features of the characteristic polynomial of the Cartan matrix of a simple Lie algebra. The characteristic polynomial is closely related with the Chebyshev polynomials of first and second kind. In addition, we…