Special cases.

[saga.git] / notation.tex

diff --git a/notation.tex b/notation.tex
index bbf7a534dbffe9efe73238de1c65bacfe5a87d6d..f2c84dd1ec0bf08c0817028aa0e55ef6d2ded9e1 100644 (file)
--- a/notation.tex
+++ b/notation.tex
@@ -10,6 +10,11 @@
 \n{$\bb R$}{the set of all real numbers}
 \n{$\bb N$}{the set of all natural numbers, including 0}
 \n{${\bb N}^+$}{the set of all positive integers}
+\n{$\O(g)$}{asymptotic~$O$: $f=\O(g)$ iff $\exists c>0: f(n)\le g(n)$ for all~$n\ge n_0$}
+\n{$\Omega(g)$}{asymptotic~$\Omega$: $f=\Omega(g)$ iff $\exists c>0: f(n)\ge g(n)$ for all~$n\ge n_0$}
+\n{$\Theta(g)$}{asymptotic~$\Theta$: $f=\Theta(g)$ iff $f=\O(g)$ and $f=\Omega(g)$}
+\n{$\widetilde\O(g)$}{$f=\widetilde\O(g)$ iff $f=\O(g\cdot\log^{\O(1)} g)$}
+\n{$\poly(n)$}{$f=\poly(n)$ iff $f=\O(n^c)$ for some $c$}
 \n{$T[u,v]$}{the path in a tree~$T$ joining vertices $u$ and $v$ \[heavy]}
 \n{$T[e]$}{the path in a tree~$T$ joining the endpoints of an~edge~$e$ \[heavy]}
 \n{$A\symdiff B$}{symetric difference of sets: $(A\setminus B) \cup (B\setminus A)$}