Pith. sign in

REVIEW 1 cited by

Forcing quasirandomness with 4-point permutations

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 2407.06869 v1 pith:ABXNM6YM submitted 2024-07-09 math.CO cs.DM

classification math.COcs.DM
keywords permutationspointquasirandom-forcingknownobjectpermutationquasirandomrandom
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

A combinatorial object is said to be quasirandom if it exhibits certain properties that are typically seen in a truly random object of the same kind. It is known that a permutation is quasirandom if and only if the pattern density of each of the twenty-four 4-point permutations is close to 1/24, which is its expected value in a random permutation. In other words, the set of all twenty-four 4-point permutations is quasirandom-forcing. Moreover, it is known that there exist sets of eight 4-point permutations that are also quasirandom-forcing. Breaking the barrier of linear dependency of perturbation gradients, we show that every quasirandom-forcing set of 4-point permutations must have cardinality at least five.

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

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

  1. Sidorenko property and forcing in regular tournaments

    math.CO 2026-02 conditional novelty 7.0 of 10

    For nearly regular tournaments, a tournament has the Sidorenko property exactly when it is transitive or a blow-up of the cyclic triangle whose three parts are transitive.

Pith tools