Pith. sign in

REVIEW

A note on Tamari intervals

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1711.05027 v1 pith:ZNNUHB7U submitted 2017-11-14 math.CO

classification math.CO
keywords intervalspolynomialsymmetrydescribedobtainedtamarivariablesaccording
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

To every partial order P, one associates a polynomial $\mathbb{D}_P$ in 4 variables that enumerates the intervals of P according to 4 parameters. Some symmetry properties of this polynomial are obtained for a specific family of posets, the Tamari lattices. A ternary symmetry is proved for the polynomial in 3 variables obtained by setting one variable to 1. Another global symmetry is conjectured. The set of synchronized intervals is described using a facet of the Newton polytope. A relation to the statistics of the canopy of binary planar trees is described.

Discussion (0). Continue with ORCID to comment.

Pith tools