%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} }% }