From 9d0164cc5eaf4d2522bc0802566ccf717b71907c Mon Sep 17 00:00:00 2001 From: Martin Mares Date: Wed, 27 Feb 2008 20:49:35 +0100 Subject: [PATCH] Updated the plan. --- PLAN | 6 ++---- notation.tex | 1 + 2 files changed, 3 insertions(+), 4 deletions(-) diff --git a/PLAN b/PLAN index 3795f32..a78f57c 100644 --- a/PLAN +++ b/PLAN @@ -29,7 +29,7 @@ o Ranking and unranking o Ranking of permutations o Ranking of k-permutations - . Permutations with no fixed point + o Permutations with no fixed point . ?? other objects ?? * Dynamic MST algorithms @@ -64,14 +64,12 @@ Models: Ranking: - the general perspective: is it only a technical trick? -- move description of the ranking set to the chapter on models? - ranking of permutations on general sets, relationship with integer sorting - mention approximation of permanent -- mention \pi[x...y] +- use \pi[x...y] Notation: -- use X+e, X-e for general sets? - \O(...) as a set? - G has to be connected, so m=O(n) - impedance mismatch in terminology: contraction of G along e vs. contraction of e. diff --git a/notation.tex b/notation.tex index 7f753f3..4b15cad 100644 --- a/notation.tex +++ b/notation.tex @@ -48,6 +48,7 @@ \n{$\(x)_b$}{$\(x)$ zero-padded to exactly $b$ bits \[bitnota]} \n{$x[i]$}{when $x\in{\bb N}$: the value of the $i$-th bit of~$x$ \[bitnota]} \n{$\pi[i]$}{when $\pi$ is a~sequence: the $i$-th element of~$\pi$, starting with $\pi[1]$ \[brackets]} +\n{$\pi[i\ldots j]$}{the subsequence $\pi[i], \pi[i+1], \ldots, \pi[j]$} \n{$\sigma^k$}{the string~$\sigma$ repeated $k$~times \[bitnota]} \n{$\0$, $\1$}{bits in a~bit string \[bitnota]} \n{$\equiv$}{congruence modulo a~given number} -- 2.39.2