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author | Norbert Preining <norbert@preining.info> | 2022-10-02 03:04:14 +0000 |
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committer | Norbert Preining <norbert@preining.info> | 2022-10-02 03:04:14 +0000 |
commit | 097f244236b682cc77c6ecf25be4150091d8daf9 (patch) | |
tree | 26998e72d2b56a87033d9fb72923258fc93ebe53 /info/mathtrip/src/ids1.tex | |
parent | 4043e29dc8ac56047ac45f872a2ea1f3031b6b05 (diff) |
CTAN sync 202210020304
Diffstat (limited to 'info/mathtrip/src/ids1.tex')
-rw-r--r-- | info/mathtrip/src/ids1.tex | 30 |
1 files changed, 30 insertions, 0 deletions
diff --git a/info/mathtrip/src/ids1.tex b/info/mathtrip/src/ids1.tex new file mode 100644 index 0000000000..349f80beb8 --- /dev/null +++ b/info/mathtrip/src/ids1.tex @@ -0,0 +1,30 @@ +%This command provides the text for the formulae written in the second +%horizontal area of the second column. +% +%The command has one parameter: +% 1) The width of the text +\newcommand\TOneIdentitiesA[1]{% + \parbox[t]{#1}{% + \TOneFormulaeFontSize + \begin{DisplayFormulae}{1}{0pt}{\TOneInterlineFormulaeA}{\BigChar}{\StyleBold} + \Fm{\binom{n}{k} = \frac{n!}{(n-k)! k!}} + \Fm{\sum_{k=0}^n \binom{n}{k} = 2^n} + \Fm{\binom{n}{k} = \binom{n}{n-k}} + \Fm{\binom{n}{k} = \frac{n}{k}\binom{n-1}{k-1}} + \Fm{\binom{n}{k} = \binom{n-1}{k} + \binom{n-1}{k-1}} + \Fm{\binom{n}{m}\binom{m}{k} = \binom{n}{k} \binom{n-k}{m-k}} + \Fm{\sum_{k=0}^n \binom{r+k}{k} = \binom{r+n+1}{n}} + \Fm{\sum_{k=0}^n \binom{k}{m} = \binom{n+1}{m+1}} + \Fm{\sum_{k=0}^n \binom{r}{k}\binom{s}{n-k} = \binom{r+s}{n}} + \Fm{\binom{n}{k} = (-1)^k \binom{k-n-1}{k}} + \Fm{\SousEnsemble{n}{1} = \SousEnsemble{n}{n} = 1} + \Fm{\SousEnsemble{n}{2} = 2^{n-1}-1} + \Fm{\SousEnsemble{n}{k} = k \SousEnsemble{n-1}{k} + \SousEnsemble{n-1}{k-1}} + \Fm{\Cycle{n}{1} = (n-1)!} + \Fm{\Cycle{n}{2} = (n-1)!H_{n-1}} + \Fm{\Cycle{n}{n} = 1} + \Fm{\Cycle{n}{k} \geq \SousEnsemble{n}{k}} + \Fm{\Cycle{n}{k} = (n-1) \Cycle{n-1}{k} + \Cycle{n-1}{k-1}} + \end{DisplayFormulae} + }% +} |