The solution of a combinatorial problem

Giacomo Lorenzoni

Abstract: A procedure is exposed in order to determine the solution of a combinatorial problem. The data of the problem are a natural N and a positive real Δ. The solution of the problem are N positive real such that the succession of the 2N-1 sums, each defined by possessing like addends the elements of one of the as many combinations of the N numbers, it can increasingly be ordered turning out that the 2N-2 successive increments are all equal to Δ.

Keywords: combinatorics; combinatorial analysis; necessity and sufficiency; deducibility; problem resolution.

INDEX
1. Preliminary positions.................................................... 1
2. The constitution of the problem.................................... 2
3. The data...................................................................... 2
4. The enunciate.............................................................. 2
5. The resolutive procedure.............................................. 3
5.1 The first argumentation........................................... 3
5.2 The second argumentation...................................... 4
5.3 The results of the two previous argumentations..... 4
5.4 The resolution.......................................................... 5
5.4.1 The determination of a solution............................ 5
5.4.2 The uniqueness of the solution.............................. 5

Date of release:  18 September 2003

Language: English

Number of downloads (from 28 June 2008)757

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