Directly influenced by Colin Rowe’s essay “Mathematics of the Ideal Villa” (1947) and Warburgian art historical tradition, John Hejduk’s nine-square grid studio exercise had an ambiguous relation to instrumentality architectural history. When was copied in many architecture schools around world as a first-year project, initiating novice student realm composition, pedagogical interpretation its ...

Let $$S=\left\langle s_1,\ldots ,s_n\right\rangle $$ be a numerical semigroup generated by the relatively prime positive integers $$s_1,\ldots ,s_n$$ . $$k\geqslant 2$$ an integer. In this paper, we consider following k-power variant of Frobenius number S defined as $$\begin{aligned} {}^{k\!}r\!\left( S\right) := \text { largest } k {-power integer not belonging to S. \end{aligned}$$ investigat...