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): 1350
