Monomial

From Maths
Jump to: navigation, search

Definition

A monomial[1] is a a polynomial consisting of "no [ilmath]+[/ilmath] sign" if you will (unless it is in the coefficient), for example:

  • [ilmath]12xy^2z[/ilmath] is a monomial
  • [ilmath](12+2j)xy^2z[/ilmath] is also a monomial (just over the complex numbers)

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

Properties

  • The degree[1] of a monomial is the sum of the powers involved.
    • For example [ilmath]xy^2z[/ilmath] is of degree [ilmath]4[/ilmath]

First theorems

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




TODO: See[1] page 70



See also

References

  1. 1.0 1.1 1.2 Combinatorics - Russell Merris