Name
Abstract | ||
|---|---|---|
We prove a general “pentagonal sieve” theorem that has corollaries such as the following. First, the number of pairs of partitions of n that have no parts in common is p ( n ) 2 − p ( n −1) 2 − p ( n −2) 2 + p ( n −5) 2 + p ( n −7) 2 −….Second, if two unlabeled rooted forests of the same number of vertices are chosen i.u.a.r., then the probability that they have no common tree is .8705… . Third, if f , g are two monic polynomials of the same degree over the field GF ( q ), then the probability that f , g are relatively prime is 1−1/ q . We give explicit involutions for the pentagonal sieve theorem, generalizing earlier mappings found by Bressoud and Zeilberger. |
Year | DOI | Venue |
|---|---|---|
1998 | 10.1006/jcta.1997.2846 | J. Comb. Theory, Ser. A |
Keywords | Field | DocType |
pentagonal number sieve | Pentagonal number theorem,Discrete mathematics,Combinatorics,Vertex (geometry),Generalization,Special number field sieve,Pentagonal number,Monic polynomial,Sieve,Coprime integers,Mathematics | Journal |
Volume | Issue | ISSN |
82 | 2 | Journal of Combinatorial Theory, Series A |
Citations | PageRank | References |
10 | 1.96 | 1 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sylvie Corteel | 1 | 266 | 36.33 |
| Carla D. Savage | 2 | 349 | 60.16 |
| Herbert S. Wilf | 3 | 498 | 172.87 |
| Doron Zeilberger | 4 | 660 | 179.97 |