This paper is about $0/1$-triangles, which are the simplest nontrivial examples of $0/1$-polytopes: convex hulls of a subset of vertices of the unit $n$-cube $I^n$. We consider the subclasses of right $0/1$-triangles, and acute $0/1$-triangles, which only have acute angles. They can be explicitly counted and enumerated, also modulo the symmetries of $I^n$.

EUDML-ID : urn:eudml:doc:287776
Mots clés:
Mots clés:

@article{702926,
     title = {Counting triangles that share their vertices with the unit $n$-cube},
     booktitle = {Applications of Mathematics 2013},
     series = {GDML\_Books},
     publisher = {Institute of Mathematics AS CR},
     address = {Prague},
     year = {2013},
     pages = {1-12},
     mrnumber = {MR3204425},
     zbl = {1340.52020},
     url = {http://dml.mathdoc.fr/item/702926}
}

Brandts, Jan; Cihangir, Apo. Counting triangles that share their vertices with the unit $n$-cube, dans Applications of Mathematics 2013, GDML_Books,  (2013), pp. 1-12. http://gdmltest.u-ga.fr/item/702926/