欧拉计划 发表于 2016-11-4 23:14:37

题目194:图形着色

Coloured Configurations

Consider graphs built with the units A:   and B:, where the units are glued along the vertical edges as in the graph.

A configuration of type (a,b,c) is a graph thus built of a units A and b units B, where the graph's vertices are coloured using up to c colours, so that no two adjacent vertices have the same colour.
The compound graph above is an example of a configuration of type (2,2,6), in fact of type (2,2,c) for all c ≥ 4.

Let N(a,b,c) be the number of configurations of type (a,b,c).
For example, N(1,0,3) = 24, N(0,2,4) = 92928 and N(2,2,3) = 20736.

Find the last 8 digits of N(25,75,1984).

题目:

考虑由单元 A:和单元 B:相连(将竖直边相连接)组成的图。比如。

我们定义类型为 (a,b,c) 图形为 a 个单元 A 和 b 个单元B组成,并且最多只使用 c 种颜色的图形,同时要求相邻的两个结点颜色不能相同。

上述的图形就是 (2,2,6) 型的,当然也是(2,2,c) ,c ≥ 4 的一个例子。

定义 N(a,b,c) 为 (a,b,c) 型图形的个数。

比如,N(1,0,3) = 24,N(0,2,4) = 92928 还有 N(2,2,3) = 20736。

请给出 N(25,75,1984) 的最后 8 位数字。

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