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Results tagged with co.combinatorics
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user 151271
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
5
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1
answer
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Number of monotone functions on a square grid
How many monotone mappings $[n] \times [n] \to [n]$ exist? Here:
$[n]$ denotes $\{1, 2, \ldots, n\}$,
Monotone means that if $x_1 \le x_2$ and $y_1 \le y_2$, then $f(x_1, y_1) \le f(x_2, y_2)$.
I'm …
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3
votes
Accepted
Number of monotone functions on a square grid
Thanks to Alex Lazar for referring me to the right keywords.
This is called something like "the number of plane partitions that fit inside the $n \times n \times n$ box", and can be computed as :
$$
P …
- 231