منابع مشابه
Generalized descent patterns in permutations and associated Hopf algebras
Descents in permutations or words are defined from the relative position of two consecutive letters. We investigate a statistic involving patterns of k consecutive letters, and show that it leads to Hopf algebras generalizing noncom-mutative symmetric functions and quasi-symmetric functions.
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It is well known that the Poisson Lie algebra is isomorphic to the Hamiltonian Lie algebra [1],[3],[13]. We show that the Poisson Lie algebra can be embedded properly in the special type Lie algebra [13]. We also generalize the Hamitonian Lie algebra using exponential functions, and we show that these Lie algebras are simple.
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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.
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This article derives characterizations and computational algorithms for continuous general gradient descent trajectories in high-dimensional parameter spaces for statistical model selection, prediction, and classification. Examples include proportional gradient shrinkage as an extension of LASSO and LARS, threshold gradient descent with right-continuous variable selectors, threshold ridge regre...
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ژورنال
عنوان ژورنال: Canadian Mathematical Bulletin
سال: 2007
ISSN: 0008-4395,1496-4287
DOI: 10.4153/cmb-2007-052-4