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Areas of triangles and Beck's theorem in planes over finite fields
Areas of triangles Beck's theorem planes over finite fields Combinatorics
2012/5/9
It is shown that any subset $E$ of a plane over a finite field $\F_q$, of cardinality $|E|>q$ determines not less than $\frac{q-1}{2}$ distinct areas of triangles, moreover once can find such triangle...
Enumeration of closed random walks in the square lattice according to their areas
Enumeration of closed random square lattice
2011/2/22
We study the area distribution of closed walks of length n, begin-ning and ending at the origin. The concept of area of a walk in the square lattice is generalized and the usefulness of the new concep...