Name
Abstract | ||
|---|---|---|
Let [n{ = {1, …, n} and let Ωn be the set of all mappings from [n{ to itself. Let f be a random uniform element of Ωn and let T(f) and B(f) denote, respectively, the least common multiple and the product of the length of the cycles of f. Harris proved in 1973 that T converges in distribution to a standard normal distribution and, in 2011, Schmutz obtained an asymptotic estimate on the logarithm of the expectation of T and B over all mappings on n nodes. We obtain analogous results for random uniform mappings on n = kr nodes with preimage sizes restricted to a set of the form {0,k}, where k = k(r) ≥ 2. This is motivated by the use of these classes of mappings as heuristic models for the statistics of polynomials of the form xk + a over the integers modulo p, with p ≡ 1 (mod k). We exhibit and discuss our numerical results on this heuristic.
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Year | DOI | Venue |
|---|---|---|
2020 | 10.1145/3378570 | ACM Transactions on Algorithms |
Keywords | DocType | Volume |
Enumeration,computations in finite fields,permutations and combinations | Journal | 16 |
Issue | ISSN | Citations |
3 | 1549-6325 | 0 |
PageRank | References | Authors |
0.34 | 0 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Rodrigo S. V. Martins | 1 | 0 | 0.34 |
| D. Panario | 2 | 39 | 6.79 |
| Claudio Qureshi | 3 | 10 | 4.48 |
| Eric Schmutz | 4 | 33 | 11.84 |