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Using certain identities and inequalities in combinatorial problems. (Romanian) Zbl 1030.05009
Summary: The author gives applications of the following combinatorial identities: \[ \sum_{k=0}^p C_m^k\cdot C_n^{p-k}= C_{m+n}^p; \] \[ \sum_{k=r}^n C_n^k\cdot C_r^{k}=C_{n}^r 2^{n-r}; \] \[ \sum\limits_{k=0}^n C_{m+k}^k\cdot 2^{n-k}+\sum\limits_{k=0}^m C_{n+k}^k\cdot 2^{m-k}=2^{m+n+1}\text{ (Banach's identity}). \]
MSC:
05A19 Combinatorial identities, bijective combinatorics
05A10 Factorials, binomial coefficients, combinatorial functions
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