MathDB

covering with rectangles with integer sides

Source: Austrian Polish 1988 APMC

April 30, 2020

rectangleinteger sidelengthscoveringcombinatorial geometrycombinatorics

Problem Statement

For a rectangle

R

with integral side lengths, denote by

D(a, b)

the number of ways of covering

R

by congruent rectangles with integral side lengths formed by a family of cuts parallel to one side of

R

. Determine the perimeter

P

of the rectangle

R

for which

\frac{D(a,b)}{a+b}

is maximal.