We have introduced the Janet's algorithm for the Stanley decomposition of a monomial ideal I ⊂ S = K[x 1 , ..., x n ] and prove that Janet's algorithm gives the squarefree Stanley decomposition of S/I for a squarefree monomial ideal I. We have also shown that the Janet's algorithm gives a partition of a simplicial complex.

Using the fixed point method, we establish a generalized Ulam Hyers stability result for the monomial functional equation in the setting of complete random p-normed spaces. As a particular case, we obtain a new stability theorem for monomial functional equations in β-normed spaces.

Let F be a flock of the quadratic cone Q: X 2=X1X3 , in PG(3, q), q even, and let 6t : X0 =xt X1 + t X2 +zt X3 , t # Fq , be the q planes defining the flock F. A flock is equivalent to a herd of ovals in PG(2, q), q even, and to a flock generalized quadrangle of order (q, q). We show that if the herd contains a monomial oval, this oval is the Segre oval. This implies a result on the existence o...

In this article, we introduce monomial irreducible representations of the special linear Lie algebra $sln$. We will show that this kind of representations have bases for which the action of the Chevalley generators of the Lie algebra on the basis elements can be given by a simple formula.

in this article, we introduce monomial irreducible representations of the special linear lie algebra $sln$. we will show that this kind of representations have bases for which the action of the chevalley generators of the lie algebra on the basis elements can be given by a simple formula.

This paper presents a formula for the multiplier ideals of a monomial space curve. The formula is obtained from a careful choice of log resolution. We construct a toric blowup of affine space in such a way that a log resolution of the monomial curve may be constructed from this toric variety in a well controlled manner. The construction exploits a theorem of González Pérez and Teissier (2002).