AVAL, J. -C.; BERGERON, F.; BERGERON, N.

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AVAL, J. -C.
Théorie des Nombres et Algorithmique Arithmétique [A2X]

BERGERON, F.

BERGERON, N.

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Advances in Mathematics. 2004, vol. 181,No.2, p. 353-367

Elsevier

Resumen en inglés

The aim of this work is to study the quotient ring R_n of the ring Q[x_1,...,x_n] over the ideal J_n generated by non-constant homogeneous quasi-symmetric functions. We prove here that the dimension of R_n is given by C_n, the n-th Catalan number. This is also the dimension of the space SH_n of super-covariant polynomials, that is defined as the orthogonal complement of J_n with respect to a given scalar product. We construct a basis for R_n whose elements are naturally indexed by Dyck paths. This allows us to understand the Hilbert series of SH_n in terms of number of Dyck paths with a given number of factors.< Leer menos

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Institut de Mathématiques de Bordeaux (IMB) - UMR 5251