The number of plane corner cuts. (English) Zbl 0955.52009
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 S. Onn and 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.
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.
Reviewer: Erhard Quaisser (Potsdam)
MSC:
| 52B05 | Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) |
| 05A99 | Enumerative combinatorics |
Citations:
Zbl 0955.52008References:
| [1] | Onn, S.; Sturmfels, B., Cutting corners, Adv. Appl. Math., 23, 29-48 (1999) · Zbl 0955.52008 |
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