Some properties of a new partial order on Dyck paths

Abstract : We introduce and study a new partial order on Dyck paths. We prove that these posets are meet-semilattices. We show that their numbers of intervals are the same as the number of bicubic planar maps. We describe an unexpected connection with the Hochschild polytopes of Saneblidze.
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https://hal.archives-ouvertes.fr/hal-01878792
Contributor : Frédéric Chapoton <>
Submitted on : Friday, September 21, 2018 - 2:36:21 PM
Last modification on : Monday, October 22, 2018 - 4:11:48 PM
Long-term archiving on : Saturday, December 22, 2018 - 4:47:37 PM

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  • HAL Id : hal-01878792, version 1
  • ARXIV : 1809.10981

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Frédéric Chapoton. Some properties of a new partial order on Dyck paths. 2018. ⟨hal-01878792⟩

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