In this paper, we find a formula for the largest integer (p-Frobenius number) such that linear equation of non-negative coefficients composed Jacobsthal triplet has at most p representations. For p=0, problem is reduced to famous Diophantine Frobenius, which called Frobenius number. We also give closed number integers (p-genus), equations have Extensions polynomial and Jacobsthal–Lucas more gen...

The classical Frobenius–Schur indicators for finite groups are character sums defined for any representation and any integer m ≥ 2. In the familiar case m = 2, the Frobenius–Schur indicator partitions the irreducible representations over the complex numbers into real, complex, and quaternionic representations. In recent years, several generalizations of these invariants have been introduced. Bu...

In a paper [1] the authors ask whether the Frobenius and the H norms are induced. There they claimed that the Frobenius norm is not induced, and consequently conjectured that the H-norm may not be induced. In this note it is shown that the Frobenius norm is induced on particular matrix spaces. It is then shown that the H-norm is in fact induced on a particular matrix-valued L1 space. NOTATION R...

Let N ≥ 2 and let 1 < a1 < · · · < aN be relatively prime integers. Frobenius number of this N-tuple is defined to be the largest positive integer that cannot be expressed as ∑ N i=1 aixi where x1, ..., xN are non-negative integers. The condition that gcd(a1, ..., aN ) = 1 implies that such number exists. The general problem of determining the Frobenius number given N and a1, ..., aN is NP-hard...

We show that given a Frobenius algebra there is a unique notion of its second quantization, which is the sum over all symmetric group quotients of n–th tensor powers, where the quotients are given by symmetric group twisted Frobenius algebras. To this end, we consider the setting of Frobenius algebras given by functors from geometric categories whose objects are endowed with geometric group act...

A finite Frobenius group is a permutation group which is transitive but not regular such that only the identity element can fix two points. Such a group can be expressed as a semidirect product G = K o H, where K is a nilpotent normal subgroup. A first-kind G-Frobenius graph is a Cayley graph on K whose connection set is an H-orbit S on K that generates K, where H is of even order or S consists...

Abstract. The semisimple Frobenius manifolds related to the Hurwitz spaces Hg,N(k1, . . . , kl) are considered. We show that the corresponding isomonodromic tau-function τI coincides with (−1/2)power of the Bergmann tau-function which was introduced in a recent work by the authors [8]. This enables us to calculate explicitly the G-function of Frobenius manifolds related to the Hurwitz spaces H0...

Frobenius pseudomonoids are higher-dimensional algebraic structures, first studied by Street [34], which categorify the classical algebraic notion of Frobenius algebra [24]. These higher algebraic structures have an important application to logic, since Frobenius pseudomonoids in the bicategory of categories, profunctors and natural transformations, for which the multiplication and unit have ri...