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A generating set of Solomon's descent algebra
- Source :
- Journal of Algebra. (1):151-158
- Publisher :
- Elsevier Science (USA).
-
Abstract
- Solomon's descent algebra is generated by sums of descent classes corresponding to certain hook shapes. This particularly implies that the ring of class functions of any finite symmetric group S n is generated by the irreducible characters corresponding to certain hook partitions of n . As another consequence, a second generating set of Solomon's descent algebra (and of the ring of class functions of S n ) is obtained related to the major index of permutations.
- Subjects :
- Discrete mathematics
Hook shape
Class (set theory)
Ring (mathematics)
Algebra and Number Theory
Mathematics::Combinatorics
Hook
Major index
Bialgebra
Combinatorics
Symmetric group
ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION
Generating set of a group
Convolution product
Descent (mathematics)
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 00218693
- Issue :
- 1
- Database :
- OpenAIRE
- Journal :
- Journal of Algebra
- Accession number :
- edsair.doi.dedup.....9477903ac4c4b42a78ab356b7c510ca8
- Full Text :
- https://doi.org/10.1016/S0021-8693(03)00069-3