Geodesic
On floors and ceilings of the \(k\)-Catalan arrangement
Marko Thiel1
1Universität Wien
The electronic journal of combinatorics, Tome 21 (2014) no. 4
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The set of dominant regions of the $k$-Catalan arrangement of a crystallographic root system $\Phi$ is a well-studied object enumerated by the Fuß-Catalan number $Cat^{(k)}(\Phi)$. It is natural to refine this enumeration by considering floors and ceilings of dominant regions. A conjecture of Armstrong states that counting dominant regions by their number of floors of a certain height gives the same distribution as counting dominant regions by their number of ceilings of the same height. We prove this conjecture using a bijection that provides even more refined enumerative information.
DOI : 10.37236/4121
Classification : 52C35, 05A15, 17B22
Mots-clés : Fuss-Catalan combinatorics, Catalan arrangement, floors, ceilings

Marko Thiel  1

1 Universität Wien 
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Marko Thiel. On floors and ceilings of the \(k\)-Catalan arrangement. The electronic journal of combinatorics, Tome 21 (2014) no. 4. doi: 10.37236/4121

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