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Let there be m doctors and n<=m patients, and let all mn possible combinations of examinations of patients by doctors take place. Then what is the minimum number of surgical ...

Discrete mathematics is the branch of mathematics dealing with objects that can assume only distinct, separated values. The term "discrete mathematics" is therefore used in ...

In continuum percolation theory, the so-called germ-grain model is an obvious generalization of both the Boolean and Boolean-Poisson models which is driven by an arbitrary ...

Two lattice points (x,y) and (x^',y^') are mutually visible if the line segment joining them contains no further lattice points. This corresponds to the requirement that ...

A plane path on a set of equally spaced lattice points, starting at the origin, where the first step is one unit to the north or south, the second step is two units to the ...

Let L=(L, ^ , v ) be a lattice, and let f,g:L->L. Then the pair (f,g) is a local polarity if and only if for each finite set X subset= L, there is a finitely generated ...

A circle having a given number of lattice points on its circumference. The Schinzel circle having n lattice points is given by the equation {(x-1/2)^2+y^2=1/45^(k-1) for n=2k ...

Let A be the area of a simply closed lattice polygon. Let B denote the number of lattice points on the polygon edges and I the number of points in the interior of the ...

Let the number of random walks on a d-D hypercubic lattice starting at the origin which never land on the same lattice point twice in n steps be denoted c_d(n). The first few ...

A Dyck path is a staircase walk from (0,0) to (n,n) that lies strictly below (but may touch) the diagonal y=x. The number of Dyck paths of order n is given by the Catalan ...