# Chvatal function

• $LaTeX: F$ is a Chvatal function (of rank 0) if it is a linear function.
• If $LaTeX: F$ and $LaTeX: G$ are Chvatal functions, then $LaTeX: aF+bG$ is a Chvatal function for any nonnegative $LaTeX: a$ and $LaTeX: b$, and its rank is $LaTeX: \max \{\mbox{rank}(F), \mbox{rank}(G)\}$. (Some require $LaTeX: a$ and $LaTeX: b$ to be rational.)
• If $LaTeX: F$ is a Chvatal function of rank $LaTeX: r$, then $LaTeX: | F |$ is a Chvatal function, and its rank is $LaTeX: r+1$ if $LaTeX: | F |$ is not equal to $LaTeX: F$.