Motivated by the classical Frobenius problem, we introduce the Frobenius poset on the integers Z, that is, for a sub-semigroup Λ of the non-negative integers (N,+), we define the order by n ≤Λ m if m− n ∈ Λ. When Λ is generated by two relatively prime integers a and b, we show that the order complex of an interval in the Frobenius poset is either contractible or homotopy equivalent to a sphere....

Let n ≥ 2 and s ≥ 1 be integers and a = (a1, . . . , an) be a relatively prime integer n-tuple. The s-Frobenius number of this ntuple, Fs(a), is defined to be the largest positive integer that cannot be represented as ∑n i=1 aixi in at least s different ways, where x1, ..., xn are non-negative integers. This natural generalization of the classical Frobenius number, F1(a), has been studied recen...

In this paper we explain the relationship between Frobenius objects in monoidal categories and adjunctions in 2-categories. Specifically, we show that every Frobenius object in a monoidal category M arises from an ambijunction (simultaneous left and right adjoints) in some 2-category D into which M fully and faithfully embeds. Since a 2D topological quantum field theory is equivalent to a commu...

In this paper, we study cyclic stabiliser codes over Fp of length dividing p + 1 for some positive integer t. We call these t-Frobenius codes or just Frobenius codes for short. We give methods to construct them and show that they have efficient decoding algorithms. An important subclass of stabiliser codes are the linear stabiliser codes. For linear Frobenius codes we have stronger results: We ...