3D Polyominoes inscribed in a rectangular prism
Abstract
We introduce a family of 3D combinatorial objects that we define as minimal 3D polyominoes inscribed in a rectanglar prism. These objects are connected sets of unitary cubic cells inscribed in a given rectangular prism and of minimal volume under this condition. They extend the concept of 2D polyominoes inscribed in a rectangle defined in a previous work. Using their geometric structure and elementary combinatorial arguments, we construct generating functions of minimal 3D polyominoes in the form of rational functions. We also obtain a number of exact formulas and recurrences for subfamilies of these polyominoes.
 Publication:

arXiv eprints
 Pub Date:
 September 2010
 arXiv:
 arXiv:1009.4859
 Bibcode:
 2010arXiv1009.4859A
 Keywords:

 Mathematics  Combinatorics;
 05A15
 EPrint:
 15 pages