We give a simple bijection between some staircase tableaux and tables of inversion. Some nice properties of the bijection allows us to define some q-Eulerian polynomials related to the staircase tableaux. We also give a combinatorial interpretation of these q-Eulerian polynomials in terms of permutations. Résumé. Nous proposons une bijection simple entre certains tableaux escalier et les tables...

the concept of comprehensive grobner bases was introduced by weispfenning. montes has proposed an efficient algorithm for computing these bases. but he has not explicitly used buchberger's criteria in his algorithm. in this paper we prove that we can apply these criteria on montes algorithm. we propose a modified version of montes algorithm and evaluate its performance via some examples.

the concept of comprehensive grobner bases was introduced by weispfenning. montes has proposed an efficient algorithm for computing these bases. but he has not explicitly used buchberger's criteria in his algorithm. in this paper we prove that we can apply these criteria on montes algorithm. we propose a modified version of montes algorithm and evaluate its performance via some examples.

Each matrix representation P: G —> GLn(K) of a finite Group G over a field K induces an action of G on the module A over the polynomial algebra A = K [ x 1 , . . . , xn]. The graded A-submodule M(P) of A generated by the orbit of (x1, ..., xn) is studied. A decomposition of MO) into generic modules is given. Relations between the numerical invariants of P and those of M(P), the latter being eff...

Bracket coefficients for polynomials are introduced. These are like specific precision floating point numbers together with error terms. Working in terms of bracket coefficients, an algorithm that computes a Grobner basis with floating point coefficients is presented, and a new criterion for determining whether a bracket coefficient is zero is proposed. Given a finite set F of polynomials with ...