  A generalised numerical semigroup (GNS) is a submonoid $S$ of $\mathbb{N}^d$
for which the complement $\mathbb{N}^d\setminus S$ is finite. The points in the
compliment $\mathbb{N}^d\setminus S$ are called gaps. A gap $F$ is considered
Frobenius allowable if there is some relaxed monomial ordering on
$\mathbb{N}^d$ with respect to which $F$ is the largest gap. We characterise
the Frobenius allowable gaps of a GNS. We extend the notions of symmetric and
irreducible numerical semigroups into GNS and show that they have analogous
properties. A GNS that has only one Frobenius allowable gap is called a
Frobenius GNS. We estimate the number of Frobenius GNS with a given Frobenius
gap $F\in\mathbb{N}^d$ and show that it is close to $\sqrt{3}^{\|F\|}$ for
large $d$. Here $\|F\|=\|(F^{(1)},\dots,F^{(d)})\|=(F^{(1)}+1)\cdots
(F^{(d)}+1)$.
