The number of plane corner cuts (Q1809521)

An \(n\)-element subset \(\lambda\) of \(\mathbb{N}^2\) which is cut off a line is called a (plane) corner cut of size \(n\). Let be \({\mathbb{N}^2\choose n}_{ \text{cut}}\) the set of corner cuts of size \(n\). [See \textit{S. Onn} and \textit{B. Sturmfels}, ibid., 29-48 (1999; above).] The authors give a generating for the number \(\#{\mathbb{N}^2\choose n}_{\text{cut}}\) and prove that there exist two positive constants \(c\) and \(c'\) such that, for all \(n>1:cn\log n<\# {\mathbb{N}^2 \choose n}_{\text{cut}}< c'n\log n\). With regard to the paper by Onn and Sturmfels this article obtains results for the special case of dimension 2.