## Counting 2-way Monotonic Terrace Forms over Rectangular Landscapes

**Authors:** Richard J. Mathar

A terrace form assigns an integer altitude to each point of a finite two-dimensional square grid
such that the maximum altitude difference between a point and its four neighbors is one.
It is 2-way monotonic if the sign of this altitude difference is zero or one for steps to the East or steps
to the South. We provide tables for the number of 2-way monotonic terrace forms as a function of grid size
and maximum altitude difference, and point at the equivalence to the number of 3-colorings of the grid.

**Comments:** 27 Pages. Added Section 6 (cut sets) and removed the inconclusive Appendix B.

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### Submission history

[v1] 2015-11-23 15:08:55

[v2] 2015-12-05 16:57:21

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