Basi di Grobner e Leggi di Raddrizzamento per le bitabelle di Young

The aim of this paper is to prove that the straightening laws for the letterplace algebra's bideterminants form a Gröbner basis for the ideal generated by Laplace expansions. Since the bideterminants can be interpretated as products of any order minors (subdeterminants) of a matrix of indeterminates, these results extends those obtained by Sturmfels and White who proved that Plucker's identities form a Gröbner basis for the ideal of identities verified only by maximal order minors. The basic ideal of our work is the idea, due to De Concini, Eisenbud and Procesi, that the general case of the minors of any order can be derived from the case of the Plucker's coordinates through a dehomogenizing morphism. In fact, it's well kwown that a Gröbner basis dehomogenizes still in a Gröbner basis provided that certain conditions on term ordering are satisfied.