Name
Abstract | ||
|---|---|---|
We introduce the notion of the descent set polynomial as an alternative way of encoding the sizes of descent classes of permutations. Descent set polynomials exhibit interesting factorization patterns. We explore the question of when particular cyclotomic factors divide these polynomials. As an instance we deduce that the proportion of odd entries in the descent set statistics in the symmetric group S"n only depends on the number on 1's in the binary expansion of n. We observe similar properties for the signed descent set statistics. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1016/j.jcta.2008.05.011 | J. Comb. Theory, Ser. A |
Keywords | Field | DocType |
descent set statistic,descent set statistics,interesting factorization pattern,type b quasisymmetric functions,cyclotomic factor,descent class,signed descent set statistic,odd entry,permutations,descent set polynomial,polynomials exhibit,binary expansion,quasisymmetric functions,cyclotomic polynomials,multivariate cd -index,signed permutations,particular cyclotomic factor,kummer's theorem,similar property,fermat primes,indexation,symmetric group,cyclotomic polynomial | Discrete mathematics,Combinatorics,Symmetric group,Polynomial,Cyclotomic polynomial,Kummer's theorem,Permutation,Factorization,Fermat number,Mathematics,Binary number | Journal |
Volume | Issue | ISSN |
116 | 2 | Journal of Combinatorial Theory, Series A |
Citations | PageRank | References |
3 | 0.65 | 10 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Denis Chebikin | 1 | 36 | 5.66 |
| Richard Ehrenborg | 2 | 233 | 48.40 |
| Pavlo Pylyavskyy | 3 | 24 | 5.20 |
| Margaret Readdy | 4 | 95 | 16.72 |