臺灣博碩士論文加值系統

在組合數論的領域中，P. Erdos曾經提出了相異冪集合的問題。而知名的 Atkinson和 Conway等數學家也各自提出了能產生相異冪集合的數列作為近似最佳解。因此，我們從圖論上著手。在本篇中我們透過一些特別類型的圖去逼近相異冪集合問題的最佳解。

P. Erdos asked a problem about the subset-sum-distinct sets. Atkinson-Negro-Santoro sequence and Conway-Guy sequence are known best solutions for problem. We treat this problem in graphs. Precisely, we consider weighted graphs such as paths, cycles, stars, and grids in order to approach the best solution.

Contents
1 Introduction 3
2 Subset Sum Distinct 4
2.1 Atkinson-Negro-Santoro sequence 6
2.2 Conway-Guy sequence 7
3 Sum Distinct Property on Graphs 11
4 Paths and Cycles 14
5 Stars 19
6 Grids 25
Reference 27

[1] Tom Bohman. A sum packing problem of Erdös and the Conway-Guy sequence. Proc.
Amer. Math. Soc., (124, 3627-3636), 1996.

[2] Steven R. Finch. Mathematical Constants, volume 1. Cambridge, 2003.

[3] The OEIS Foundation. The on-line encyclopedia of integer sequences, http://oeis.org/
2013.

[4] Alexander Rosa. Theory and Practice of Combinatorics, volume 12. North Holland,
1982.