Identities and bases in the hypoplactic monoid

On the hypoplactic monoid

Cet article pr esente une etude combinatoire du mono de hypoplaxique. Apr es avoir rappel e les d eenitions classiques, nous exhibons un algorithme qui est l'analogue hypoplaxique de l'algorithme de Schensted puis nous donnons un certain nombre de propri et es int eressantes de ce mono de. Abstract This paper presents a combinatorial study of the hypoplactic monoid. After having recalled the ba...

On Grr Obner Bases in Monoid and Group Rings

Following Buchberger's approach to computing a Grr obner basis of a polynomial ideal in polynomial rings, a completion procedure for nitely generated right ideals in ZH] is given, where H is an ordered monoid presented by a nite, convergent semi{Thue system ((; T). Taking a nite set F ZH] we get a (possibly innnite) basis of the right ideal generated by F , such that using this basis we have un...

On Gröbner Bases in Monoid and Group Rings

On Gröbner bases in monoid and group rings

On Binomial Identities in Arbitrary Bases

We first extend the digital binomial identity as given by Nguyen et al. to an identity in an arbitrary base b, by introducing the b-ary binomial coefficients. Then, we study the properties of these coefficients such as their orthogonality, their link with Lucas’ theorem and their extension to multinomial coefficients. Finally, we analyze the structure of the corresponding b-ary Pascal-like tria...