In this very nice read, the authors present us with a new characteristic \(p\) invariant for a local ring \(R\), which they termed the Frobenius complexity. Suppose \(A=\bigoplus\limits_{d=0}^{\infty} A_d\) is a graded ring, not necessarily commutative. Let \(G_d(A)\) be the subring of \(A\) generated in degree \(\leq d\) and \(k_d\) denote the minimal number of generators of \(G_d(A)\). The complexity sequence of \(A\) is given by \(\{k_d-k_{d-1}\}_{d \geq 0}\) and the complexity of \(A\) is \(cx(A)=\text{inf}\{n \mid k_d-k_{d-1}=O(n^d)\}\). The Frobenius complexity of a local ring \(R\) of characteristic \(p\) is defined as follows, \(cx_F(R):=\log_p(cx(\mathcal{F}(E)))\), where \(\mathcal{F}(E)\) is the ring of Frobenius operators on the injective hull of the residue field of \(R\). They first investigate the complexity of the skew \(R\) algebra \(T(R[x_1, \ldots x_d]):=T(\mathcal{R})\) defined by M. Katzman et al. [Math. Proc. Camb. Philos. Soc. 157, No. 1, 151–167 (2014; Zbl 1332.13005)]. They show that for \(0 \leq d \leq 2\), \(cx(T(\mathcal{R}))=0\) and for \(d=3\), \(cx(T(\mathcal{R}))=\displaystyle\frac{p(p+1)}{2}\). They also describe an algorithm to compute \(cx(T(\mathcal{R}))\) for \(d \geq 4\), and expressly compute \(cx(T(\mathcal{R}))=5+\sqrt{5}\) for \(d=4\) and \(p=2\). Using a theorem of Katzman, Schwede, Singh and Zhang in the complete normal setting which states that \(\mathcal{F}(E) \cong T(\mathcal{R}(\omega))\) for \(\omega\) the canonical ideal of \(R\), they show that if \(R\) is \(\mathbb{Q}\)-Gorenstein with \(p \mid \text{ord}(\omega)\), then \(cx_F(R)=0\). They further show in the complete normal setting that if \(\mathcal{R}(\omega)\) is a finitely generated \(R\)-algebra, then \(cx_F(R)\) is finite. They conclude the paper, showing that the Frobenius complexity of the \(T\)-construction of the Segre product of \(K[x_1, \cdots, x_d]\) and \(K[y_1, \ldots, y_{d-1}]\) is the same as the Frobenius complexity of \(T(K[x_1, \ldots, x_d])\).