Abstract:
For any three-index planar transportation polytope (3-PTP) $M$
of order $m\times n\times k$ and dimensionality $d$,
we give a three-index axial transportation polytope (3-ATP)
$M'$ of order $mk\times nk\times mn$, with a
$d$-face which is combinatorially equivalent to the polytope $M$,
and vice versa, for any 3-ATP $M$ of order
$m\times n\times k$ we give a 3-PTP $M'$ of order
$(m+1)\times (n+1)\times (k+1)$, with
an $(mnk-m-n-k+2)$-face which is combinatorially equivalent to the polytope
$M$. With the use of these results, we present a series of new properties
of three-index transportation polytopes.
The research was supported by the Foundation for Basic Research of Republic Byelarus,
grant $\Phi$95-70.