Pith. sign in

REVIEW 1 cited by

Linear Intervals in the Tamari and the Dyck Lattices and in the alt-Tamari Posets

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

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 2209.00418 v2 pith:53FA5GYK submitted 2022-09-01 math.CO

Clément Chenevière (IRMA , RUB) This is my paper · ORCID
classification math.CO
keywords alt-tamaridycklatticesposetsdeltaintervalslineartamari
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

We count the number of linear intervals in the Tamari and the Dyck lattices according to their height, using generating series and Lagrange inversion. Surprisingly, these numbers are the same in both lattices. We define a new family of posets on Dyck paths, which we call alt-Tamari posets. Each alt-Tamari poset depends on the choice of an increment function delta in {0,1}^n. We recover the Tamari and the Dyck lattices as extreme cases with delta = 1 and delta = 0, respectively. We prove that all the alt-Tamari posets have the same number of linear intervals of any given height.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Affine Tamari Lattice

    math.CO 2025-02 conditional novelty 8.0 of 10

    New cyclic and affine Tamari lattices of sizes Catalan Bn and Dn are constructed and shown to govern maximal green sequence lengths for path algebras of oriented cycles.

Pith tools