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A self-avoiding walk in which steps may be to the left, right, or straight ahead after a vertical step, but only straight ahead or to the left after a horizontal step. A ...

A cellular automaton is a collection of "colored" cells on a grid of specified shape that evolves through a number of discrete time steps according to a set of rules based on ...

Let L be a lattice (or a bounded lattice or a complemented lattice, etc.), and let C_L be the covering relation of L: C_L={(x,y) in L^2|x covers y or y covers x}. Then C_L is ...

A parallelogram polyomino is a polyomino such that the intersection with every line perpendicular to the main diagonal is a connected segment. The number of parallelogram ...

A lattice polygon consisting of a closed self-avoiding walk on a square lattice. The perimeter, horizontal perimeter, vertical perimeter, and area are all well-defined for ...

A stack polyomino is a self-avoiding convex polyomino containing two adjacent corners of its minimal bounding rectangle. The number of stack polyominoes with perimeter 2n+4 ...

Define the minimal bounding rectangle as the smallest rectangle containing a given lattice polygon. If the perimeter of the lattice polygon is equal to that of its minimal ...

Let (L,<=) be any complete lattice. Suppose f:L->L is monotone increasing (or isotone), i.e., for all x,y in L, x<=y implies f(x)<=f(y). Then the set of all fixed points of f ...

Let Delta denote an integral convex polytope of dimension n in a lattice M, and let l_Delta(k) denote the number of lattice points in Delta dilated by a factor of the integer ...

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 ...