### Citations

1192 | Enumerative combinatorics - Stanley - 1999 |

678 | Reflection groups and Coxeter groups - Humphreys - 1990 |

337 | Free Lie algebras - Reutenauer - 1993 |

113 | A Mackey formula in the group ring of a Coxeter group - Solomon - 1976 |

106 | Advanced determinant calculus, Séminaire Lotharingien Combin - Krattenthaler - 1999 |

52 | Normalizers of parabolic subgroups of reflection groups - Howlett - 1980 |

51 | A decomposition of the descent algebra of a finite Coxeter group,
- Bergeron, Bergeron, et al.
- 1992
(Show Context)
Citation Context ... ∑ w∈DJ w, we get xS\K = ∑ J⊆K yJ , and hence by Möbius inversion formula yJ = ∑ K⊆J (−1)|J\K|xS\K . The descent algebra is a well studied object on the borderline of combinatorics and algebra ([1], =-=[2]-=-, [4]). Especially the descent algebra relative to the Coxeter system of the symmetric group 2 (An, SAn = {t1, . . . , tn}), where ti is the transposition (i i+1) ([7], [11]). Thibon determined the ei... |

9 |
A Symmetry of the Descent Algebra of a Finite Coxeter
- Blessenohl, Hohlweg, et al.
- 2005
(Show Context)
Citation Context ...DJ w, we get xS\K = ∑ J⊆K yJ , and hence by Möbius inversion formula yJ = ∑ K⊆J (−1)|J\K|xS\K . The descent algebra is a well studied object on the borderline of combinatorics and algebra ([1], [2], =-=[4]-=-). Especially the descent algebra relative to the Coxeter system of the symmetric group 2 (An, SAn = {t1, . . . , tn}), where ti is the transposition (i i+1) ([7], [11]). Thibon determined the eigenva... |

9 | Semigroups, rings, and Markov chains,
- Brown
- 2000
(Show Context)
Citation Context ... J⊆SAn qMaj(J) yJ ∈ R(q)[ΞAn ], where Maj(J) := ∑ j∈{i∈[n] | ti∈J} j. In [17], Schocker worked on the descent algebra of the symmetric group. Using hyperplanes arrangement and random walk properties (=-=[5]-=-, [6]), Brown determined the condition of diagonalizability of the action of element of the descent algebra of finite Coxeter group, and gave a remarkable approach of the eigenvalues and corresponding... |

6 | Spectra of symmetrized shuffling operators - Reiner, Saliola, et al. |

6 | Realizability of a Model - Zagier |

4 |
Symbolic Manipulation for the Study of the Descent Algebra of Finite Coxeter Groups
- Bergeron, Bergeron
- 1992
(Show Context)
Citation Context ...yJ := ∑ w∈DJ w, we get xS\K = ∑ J⊆K yJ , and hence by Möbius inversion formula yJ = ∑ K⊆J (−1)|J\K|xS\K . The descent algebra is a well studied object on the borderline of combinatorics and algebra (=-=[1]-=-, [2], [4]). Especially the descent algebra relative to the Coxeter system of the symmetric group 2 (An, SAn = {t1, . . . , tn}), where ti is the transposition (i i+1) ([7], [11]). Thibon determined t... |

4 | The Symmetric Group Representations - SAGAN |

4 | Bilinear Form of Real Configuration - Varchenko - 1993 |

3 |
Noncommutative Symmetric Functions II
- Krob, Leclerc, et al.
- 1997
(Show Context)
Citation Context ...inatorics and algebra ([1], [2], [4]). Especially the descent algebra relative to the Coxeter system of the symmetric group 2 (An, SAn = {t1, . . . , tn}), where ti is the transposition (i i+1) ([7], =-=[11]-=-). Thibon determined the eigenvalues and their multiplicities of the action of the element [10, Theorem 56]∑ J⊆SAn qMaj(J) yJ ∈ R(q)[ΞAn ], where Maj(J) := ∑ j∈{i∈[n] | ti∈J} j. In [17], Schocker work... |

2 | The Distance Spectra of Cayley Graphs - Renteln - 2011 |

1 |
Semigroup and Ring Theoretical Methods
- Brown
- 2003
(Show Context)
Citation Context ...n qMaj(J) yJ ∈ R(q)[ΞAn ], where Maj(J) := ∑ j∈{i∈[n] | ti∈J} j. In [17], Schocker worked on the descent algebra of the symmetric group. Using hyperplanes arrangement and random walk properties ([5], =-=[6]-=-), Brown determined the condition of diagonalizability of the action of element of the descent algebra of finite Coxeter group, and gave a remarkable approach of the eigenvalues and corresponding mult... |

1 |
The Descent Algebra of the Symmetric
- Schocker
(Show Context)
Citation Context ... (i i+1) ([7], [11]). Thibon determined the eigenvalues and their multiplicities of the action of the element [10, Theorem 56]∑ J⊆SAn qMaj(J) yJ ∈ R(q)[ΞAn ], where Maj(J) := ∑ j∈{i∈[n] | ti∈J} j. In =-=[17]-=-, Schocker worked on the descent algebra of the symmetric group. Using hyperplanes arrangement and random walk properties ([5], [6]), Brown determined the condition of diagonalizability of the action ... |