Pith. sign in

REVIEW 1 cited by

On the Number of Walks in a Triangular Domain

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 1402.4448 v2 pith:2SHZF4JY submitted 2014-02-18 math.CO

Paul RG Mortimer , Thomas Prellberg This is my paper · ORCID
classification math.CO
keywords domainwalkstriangularfixedformulalatticepathsstarting
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

We consider walks on a triangular domain that is a subset of the triangular lattice. We then specialise this by dividing the lattice into two directed sublattices with different weights. Our central result is an explicit formula for the generating function of walks starting at a fixed point in this domain and ending anywhere within the domain. Intriguingly, the specialisation of this formula to walks starting in a fixed corner of the triangle shows that these are equinumerous to two-coloured Motzkin paths, and two-coloured three-candidate Ballot paths, in a strip of finite 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. An explicit power series result for the two type ASEP

    math.CO 2025-07 reject novelty 4.0 of 10

    The paper states a power series formula for the generating function of the two-type ASEP with configuration (2,1,0,...,0), but the proof of the main decomposition is missing.

Pith tools