Dan asks ...
Let T denote the torus obtained by identifying each pair of opposite edges of a regular hexagon.
How does this work? I can't get the edges to match up. Scott asks ...
Is there a nice general formula or a good approximation for the number of nondecreasing sequences in N^k, for integers N and k ?
For an exact formula: The 1D case is already answered, a quotient of factorials. Based on experiments done long long ago, at an Institute far far away, the 2D case seems to be a product of something like the 1D answers. Strict vs. non-strict vs. semi-strict perturbs the formulas slightly. This also worked for rectangles, MxN. But I couldn't find a similar answer for the 3D case. I always figured there was a tie-in with linear and planar partitions having a nice generating function, while cubic partitions don't seem to have one. Dave Wilson asks ...
What is the probability that a randomly chosen square is in a unomino (I find only one page on the web with that word!)?
I think Gardner's columns used "monomino". Rich