3D Polyominoes inscribed in a rectangular prism

Details 3D Polyominoes inscribed in a rectangular prism 3D Polyominoes inscribed in a rectangular prism

2010-09-24

arxiv.org/abs/1009.4859v1

Mathematics

Combinatorics

15 pages

Scientific paper

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 sub-families of these polyominoes.

Affiliated with

Also associated with

No associations

Rating

3D Polyominoes inscribed in a rectangular prism does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with 3D Polyominoes inscribed in a rectangular prism, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and 3D Polyominoes inscribed in a rectangular prism will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-274636