MA-351 Homework 1

Due at 4:59pm in my mailbox in HA 245, Thursday, September 11, 2008


Calculations necessary for these problems may be done either by hand or with Maple. Solutions may be submitted in person in class, or you may email an ASCII text, Maple Worksheet (.mws), html, or postscipt/pdf-formatted document to me.
Note my office hours on my schedule.

    1. Derive the linear recurrence for Fibonacci's rabbits' problem with the change that each pair of rabbits gives birth to three pairs of rabbits instead of one.
    2. Derive a "closed form" solution for the above recurrence.

  2. Please give a formula in terms of n for the diameter of the (undirected) n by n toric mesh graph and justify your answer.

  3. Consider the 5-dimensional hypercube as presented in class. In class the vertices were the integers from 1 to 32. The task is to relabel the vertices in the drawing as 5-digit binary numbers (sequences of 5 integers in {0,1}) in such a way that the Hamming distance between adjacent vertices is exactly one.

    5-D Hypercube