Geodesic
Statistics of blocks in \(k\)-divisible non-crossing partitions
Octavio Arizmendi1
1Saarland University
The electronic journal of combinatorics, Tome 19 (2012) no. 2
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We derive a formula for the expected number of blocks of a given size from a non-crossing partition chosen uniformly at random. Moreover, we refine this result subject to the restriction of having a number of blocks given.Furthermore, we generalize to $k$-divisible partitions. In particular, we find that, asymptotically, the expected number of blocks of size $t$ of a $k$-divisible non-crossing partition of $nk$ elements chosen uniformly at random is $\frac{kn+1}{(k+1)^{t+1}}$. Similar results are obtained for type $B$ and type $D$ non-crossing partitions of Armstrong.
DOI : 10.37236/2431
Classification : 62K99, 62K10

Octavio Arizmendi  1

1 Saarland University 
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     title = {Statistics of blocks in \(k\)-divisible non-crossing partitions},
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Octavio Arizmendi. Statistics of blocks in \(k\)-divisible non-crossing partitions. The electronic journal of combinatorics, Tome 19 (2012) no. 2. doi: 10.37236/2431

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