Height Functions
For some classes of tilings on a regular grid in two dimensions, it is possible to define a height function associating an integer to the nodes of the grid. For instance, draw a chessboard, fix a node with height 0, then for any node there is a path from to it. On this path define the height of each node (i.e. corners of the squares) to be the height of the previous node plus one if the square on the right of the path from to is black, and minus one otherwise.
More details can be found in Kenyon & Okounkov (2005).
Read more about this topic: Domino Tiling
Famous quotes containing the words height and/or functions:
“Men often treat others worse than they treat themselves, but they rarely treat anyone better. It is the height of folly to expect consideration and decency from a person who mistreats himself.”
—Thomas Szasz (b. 1920)
“In today’s world parents find themselves at the mercy of a society which imposes pressures and priorities that allow neither time nor place for meaningful activities and relations between children and adults, which downgrade the role of parents and the functions of parenthood, and which prevent the parent from doing things he wants to do as a guide, friend, and companion to his children.”
—Urie Bronfenbrenner (b. 1917)