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Some properties of a new partial order on Dyck paths

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arxiv 1809.10981 v1 pith:ME24QAR5 submitted 2018-09-28 math.CO

classification math.CO
keywords dyckorderpartialpathsbicubicconnectiondescribehochschild
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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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