A bijective proof of Cassini's Fibonacci identity
نویسندگان
چکیده
can be easily proved by either induction, Binet's formula, or ([1, p. 80]) by taking determinants in In this paper we give a bijective proof, based upon the following combinatorial interpretation of the Fibonacci numbers. Proof of (1). Let e = (2,..., 2); define the bijection ~r: A(n)×A(n)\(e, e)-~ A(n-1) ×A(n + 1)\(e,e) as follows. Let [bs)]eA(n) × A(n) and look for the first 1 in Case I. The first 1 is an ak. Delete ak = 1 from the first vector and insert it between bk-1 and bk in the second vector.
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 58 شماره
صفحات -
تاریخ انتشار 1986