Zobrazeno 1 - 10
of 166
pro vyhledávání: '"Novelli, J"'
Autor:
Novelli, J. -C., Thibon, J. -Y.
Publikováno v:
Advances in Applied Mathematics 117 (2020) 102019
The m-Tamari lattice of F. Bergeron is an analogue of the clasical Tamari order defined on objects counted by Fuss-Catalan numbers, such as m-Dyck paths or (m+1)-ary trees. On another hand, the Tamari order is related to the product in the Loday-Ronc
Externí odkaz:
http://arxiv.org/abs/1403.5962
The Hopf algebra of word-quasi-symmetric functions ($\WQSym$), a noncommutative generalization of the Hopf algebra of quasi-symmetric functions, can be endowed with an internal product that has several compatibility properties with the other operatio
Externí odkaz:
http://arxiv.org/abs/1101.0725
We construct explicit polynomial realizations of some combinatorial Hopf algebras based on various kind of trees or forests, and some more general classes of graphs, ranging from the Connes-Kreimer algebra to an algebra of labelled forests isomorphic
Externí odkaz:
http://arxiv.org/abs/1009.2067
Publikováno v:
J. Algebraic Combin. 33 (2011), 277-312
We extend to several combinatorial Hopf algebras the endomorphism of symmetric functions sending the first power-sum to zero and leaving the other ones invariant. As a transformation of alphabets, this is the (1-E)-transform, where E is the exponenti
Externí odkaz:
http://arxiv.org/abs/0912.0184
Publikováno v:
European Journal of Combinatorics 32 (2011), 618-627
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 noncommutative symmetric
Externí odkaz:
http://arxiv.org/abs/0911.5615
Publikováno v:
J. Algebraic Combin. 28 (2008), no. 1, 65--95
We propose several constructions of commutative or cocommutative Hopf algebras based on various combinatorial structures, and investigate the relations between them. A commutative Hopf algebra of permutations is obtained by a general construction bas
Externí odkaz:
http://arxiv.org/abs/math/0605262
Autor:
Novelli, J. -C., Thibon, J. -Y.
We realize several combinatorial Hopf algebras based on set compositions, plane trees and segmented compositions in terms of noncommutative polynomials in infinitely many variables. For each of them, we describe a trialgebra structure, an internal pr
Externí odkaz:
http://arxiv.org/abs/math/0605061
A result of Foata and Schutzenberger states that two statistics on permutations, the number of inversions and the inverse major index, have the same distribution on a descent class. We give a multivariate generalization of this property: the sorted v
Externí odkaz:
http://arxiv.org/abs/math/0605060
Publikováno v:
Advances in Mathematics 205 (2006), 504-548
After reformulating the representation theory of 0-Hecke algebras in an appropriate family of Yang-Baxter bases, we investigate certain specializations of the Ariki-Koike algebras, obtained by setting q=0 in a suitably normalized version of Shoji's p
Externí odkaz:
http://arxiv.org/abs/math/0506546
We propose several constructions of commutative or cocommutative Hopf algebras based on various combinatorial structures, and investigate the relations between them. A commutative Hopf algebra of permutations is obtained by a general construction bas
Externí odkaz:
http://arxiv.org/abs/math/0502456