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10
votes
2answers
484 views

How many triangulations of the genus $g$ surface on $n$ vertices?

By "a triangulation of $X$", I mean a simplicial complex whose geometric realization is homeomorphic to $X$. Tutte showed that the number of combinatorially distinct triangulations $t(n)$ of the ...
4
votes
1answer
176 views

Reference request: enumeration under group action

Is there a reference for the following lemma (which is useful in counting unlabeled k-trees)? It seems to me that it should be known, but I haven't been able to find it anywhere. Let $G$ be a finite ...
4
votes
1answer
136 views

Principal Order Ideals in the Weak Bruhat Order

Let $\sigma\in S_n$ be a permutation on $n$ elements, and $\mathrm{Inv}(\sigma):=\{(i,j) : 1\leq i<j\leq n\text{ and }\sigma(i)>\sigma(j)\}$ be its set of inversions. In the weak order on ...