REVIEW 5 cited by
Cycle type of random permutations: A toolkit
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
read the original abstract
We prove a number of results, new and old, about the cycle type of a random permutation on S_n. Underlying our analysis is the idea that the number of cycles of size k is roughly Poisson distributed with parameter 1/k. In particular, we establish strong results about the distribution of the number of cycles whose lengths lie in a fixed but arbitrary set I. Our techniques are motivated by the theory of sieves in number theory.
Forward citations
Cited by 5 Pith papers
-
Classical and quantum algorithms for characters of the symmetric group
A matrix product state algorithm and a polynomial-size quantum circuit are presented for computing and sampling symmetric group characters, plus a weak-to-strong simulation reduction for granular distributions.
-
Minimum degree edge-disjoint Hamilton cycles in random directed graphs
For p ≥ log^15 n / n, the random digraph D_{n,p} almost surely contains exactly δ±(D_{n,p}) edge-disjoint Hamilton cycles.
-
Permutation theory governs long-term dynamics of critical Boolean networks
For critical K=1 Boolean networks, attractor lengths are governed by the order of the permutation induced by feedback loops, yielding typical maximum lengths exp[(1/2)ln^2 N], extremal lengths exp[sqrt(N ln N)], and m...
-
Crystalline Spectral Form Factors
Strong level repulsion produces damped crystalline oscillations of the spectral form factor, with a Debye-Waller suppression, a new plateau time scale t* ≈ t_H sqrt(β/4), and predictable derivative singularities.
-
Groupoid Cardinality and Random Permutations
The Cycle Length Lemma for random permutations is derived from an equivalence of groupoids, giving a categorified proof of a known result.
Discussion (0). Continue with ORCID to comment.