منابع مشابه
Homomorphisms between Solomon's Descent Algebras
In a previous paper (see Garsia-Reutenauer [2]), we have studied algebraic properties of the descent algebras Σ n , and shown how these are related to the canonical decomposition of the free Lie algebra corresponding to a version of Poincaré-Birkhoff-Witt's theorem. In the present paper, we study homomorphisms between these algebras Σ n. The existence of these homomorphisms was suggested by pro...
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We show that the notion of parkization of a word, a variant of the classical standardization, allows to introduce an internal product on the Hopf algebra of parking functions. Its Catalan subalgebra is stable under this operation and contains the descent algebra as a left ideal.
متن کاملDescent Algebras, Hyperplane Arrangements, and Shuuing Cards
This note establishes a connection between Solomon's descent algebras and the theory of hyperplane arrangements. It is shown that card-shu ing measures on Coxeter groups, originally de ned in terms of descent algebras, have an elegant combinatorial description in terms of randomwalk on the chambers of hyperplane arrangements. As a corollary, a positivity conjecture of Fulman is proved. 2
متن کاملDescent Algebras , Hyperplane Arrangements , and Shuffling Cards
Abstract Two notions of riffle shuffling on finite Coxeter groups are given: one using Solomon’s descent algebra and another using random walk on chambers of hyperplane arrangements. These definitions coincide for types A,B,H3, and rank two groups. Both notions satisfy a convolution property and have the same simple eigenvalues. The hyperplane definition is especially natural and satisfies a po...
متن کاملErrata to " Hyperplane Arrangements and Descent Algebras "
Hyperplane arrangements and descent algebras Franco V Saliola saliola-DesAlgLectureNotes.pdf version of 10 January 2006 Errata and addenda by Darij Grinberg I will refer to the results appearing in the article " A Hyperplane arrangements and descent algebras " by the numbers under which they appear in this article. 6. Errata • Various places (for example, §2.1): You use the notations ⊆ and ⊂ sy...
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ژورنال
عنوان ژورنال: Algebras and Representation Theory
سال: 2008
ISSN: 1386-923X,1572-9079
DOI: 10.1007/s10468-008-9090-9