Faultfree Tromino Tilings of Rectangles

Details Faultfree Tromino Tilings of Rectangles Faultfree Tromino Tilings of Rectangles

2006-10-30

arxiv.org/abs/math/0610925v1

Mathematics

Combinatorics

34 pages, 17 figures

Scientific paper

In this paper we consider faultfree tromino tilings of rectangles and characterize rectangles that admit such tilings. We introduce the notion of {\it crossing numbers} for tilings and derive bounds on the crossing numbers of faultfree tilings. We develop an iterative scheme for generating faultfree tromino tilings for rectangles and derive the closed form expression for the exact number of faultfree tromino tilings for $4\times3t$ rectangles and the exact generating function for $5\times 3t$ rectangles, $t\geq 1$. Our iterative scheme generalizes to arbitrary rectangles; for $6\times 6t$ and $7\times 6t$ rectangles, $t\geq 1$, we derive generating functions for estimating lower bounds on the number of faultfree tilings. We also derive an upper bound on the number of tromino tilings of an $m\times n$ rectangle, where $3|mn$ and $m,n>0$.

Affiliated with

Also associated with

No associations

Rating

Faultfree Tromino Tilings of Rectangles 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 Faultfree Tromino Tilings of Rectangles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Faultfree Tromino Tilings of Rectangles will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-231134