Monomial

Definition

A monomial is a a polynomial consisting of "no $+$ sign" if you will (unless it is in the coefficient), for example:

• $12xy^2z$ is a monomial
• $(12+2j)xy^2z$ is also a monomial (just over the complex numbers)

In short, it is a polynomial of just one term.

Properties

• The degree of a monomial is the sum of the powers involved.
  • For example $xy^2z$ is of degree $4$

First theorems

[Expand]

Theorem: There are ${}^{n+k-1}C_n$ monomials of degree $n$ in the $k$ variables $x_1,x_2,\cdots,x_k$

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TODO: See page 70

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See also

• Monomial symmetric function
• Combinations (operator)
• Permutations (operator)