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In this section we suppose a fixed monomial ordering, which will not be defined explicitly. en.wikipedia.org

The most common polynomial basis is the monomial basis consisting of all monomials. en.wikipedia.org

The remainder of this article assumes the first meaning of monomial. en.wikipedia.org

Some groups have the property that all of their irreducible representations are monomial, the so-called monomial groups. en.wikipedia.org

A monomial in the first sense is also a monomial in the second sense, because the multiplication by 1 is allowed. en.wikipedia.org

This is for instance the case when considering a monomial basis of a polynomial ring, or a monomial ordering of that basis. en.wikipedia.org

Alternatively, one may define it as a representation whose image is in the monomial matrices. en.wikipedia.org

Let the coefficient of this term be, then is either zero or a symmetric polynomial with a strictly smaller leading monomial. en.wikipedia.org

Monomial degree is fundamental to the theory of univariate and multivariate polynomials. en.wikipedia.org

The algebra is unital if one takes the empty product as a monomial. en.wikipedia.org

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