MathDB

Let

k

\ell

and

m

be positive integers. Let

ABCDEF

be a hexagon that has a center of symmetry whose angles are all

120^\circ

and let its sidelengths be

AB=k

BC=\ell

and

CD=m

. Let

f(k,\ell,m)

denote the number of ways we can partition hexagon

ABCDEF

into rhombi with unit sides and an angle of

120^\circ

. Prove that by fixing

\ell

and

m

, there exists polynomial

g_{\ell,m}

such that

f(k,\ell,m)=g_{\ell,m}(k)

for every positive integer

k

, and find the degree of

g_{\ell,m}

in terms of

\ell

and

m

. Submitted by Zoltán Gyenes, Budapest

A. 851