Congruences for Catalan and Motzkin numbers and related sequences

Bruce E. Sagan (Michigan State U.); Emeric Deutsch (Polytechnic U.)

Congruences for Catalan and Motzkin numbers and related sequences

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 math/0407326 v1 pith:UMTI5UCN submitted 2004-07-19 math.CO

Emeric Deutsch (Polytechnic U.) , Bruce E. Sagan (Michigan State U.) This is my paper · ORCID

classification math.CO

keywords sequencesbinomialcatalancoefficientscongruencesmotzkinnumbersrelated

verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments

read the original abstract

We prove various congruences for Catalan and Motzkin numbers as well as related sequences. The common thread is that all these sequences can be expressed in terms of binomial coefficients. Our techniques are combinatorial and algebraic: group actions, induction, and Lucas' congruence for binomial coefficients come into play. A number of our results settle conjectures of Benoit Cloitre and Reinhard Zumkeller. The Thue-Morse sequence appears in several contexts.

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

Factoring Catalan numbers
math.NT 2019-08 conditional novelty 2.0 of 10

The paper shows a prime p contributes to the exponent of Cat(n) once for each k with n mod p^k strictly between p^k/2 and p^k-1, a direct consequence of Legendre's formula.

Pith tools