Frobenius is generally considered the creator of character theory finite groups. This achievement came from study group determinant, which determinant a matrix coming regular representation. We generalize several Frobenius’ results about and use them to find new formulation supercharacter in terms factorizations determinant.

Let X be a projective curve of genus 2 over an algebraically closed field of characteristic 2. The Frobenius map on X induces a rational map on the moduli space of rank-2 bundles. We show that up to isomorphism, there is only one (up to tensoring by an order two line bundle) semi-stable vector bundle of rank 2 with determinant equal to a theta characteristic whose Frobenius pull-back is not sta...

The sign-real and the sign-complex spectral radius, also called the generalized spectral radius, proved to be an interesting generalization of the classical Perron-Frobenius theory (for nonnegative matrices) to general real and to general complex matrices, respectively. Especially the generalization of the well-known Collatz-Wielandt max-min characterization shows one of the many one-to-one cor...

Fluctuations of the mean field of a globally coupled dynamical systems are discussed. The origin of hidden coherence is related with the instability of the fixed point solution of the self-consistent Perron-Frobenius equation. Collective dynamics in globally coupled tent maps are re-examined, both with the help of direct simulation and the Perron-Frobenius equation. Collective chaos in a single...

Let X be a projective curve of genus 2 over an algebraically closed field of characteristic 2. The Frobenius map on X induces a rational map on the moduli scheme of rank-2 bundles. We show that up to isomorphism, there is only one (up to tensoring by an order two line bundle) semi-stable vector bundle of rank 2 (with determinant equal to a theta characteristic) whose Frobenius pull-back is not ...

This paper is well designed to set-up some new identities related generalized Apostol-type Hermite-based-Frobenius-Genocchi polynomials and by applying the generating functions, we derive implicit summation formulae symmetric identities. Further a relationship between Array-type polynomials, Bernoulli Frobenius-Genocchi also established.

Given a set of positive integers A = {a1, . . . , ad} with gcd(a1, . . . , ad) = 1, we call an integer n representable if there exist nonnegative integers m1, . . . ,md such that n = m1a1 + · · ·+ mdad . The linear diophantine problem of Frobenius asks for the largest integer which is not representable. We call this largest integer the Frobenius number g(a1, . . . , ad). One fact which makes th...

Let N ≥ 2 and let 1 < a1 < · · · < aN be relatively prime integers. The Frobenius number of this N -tuple is defined to be the largest positive integer that has no representation as PN i=1 aixi where x1, ..., xN are nonnegative integers. More generally, the s-Frobenius number is defined to be the largest positive integer that has precisely s distinct representations like this. We use techniques...

For a nonnegative integer p, we give explicit formulas for the p-Frobenius number and p-genus of generalized Fibonacci numerical semigroups. Here, p-numerical semigroup Sp is defined as set integers whose integral linear combinations given positive a1,a2,…,ak are expressed in more than p ways. When p=0, S0 with 0-Frobenius 0-genus original Frobenius genus. In this paper, consider involving Jaco...