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Probability and Algorithms
Caltech CS150, Winter 2006
Leonard J. Schulman
TA: ChihKai (Kevin) Ko.
Problem set 5
Out Wednesday February 22. Due Monday March 6.
Week 6 reading: MU 6.76.8, 7.17.4, proof of the PerronFrobenius theorem in notes of Andries
Brouwer on the class website.
This assignment is longer than usual so I’m allowing two weeks for it.
Please get started early
though. I haven’t assigned work on the PerronFrobenius theorem but it is an important theorem
with an interesting proof, and well worth learning. (You can also ±nd the proof elsewhere, e.g., some
notes online by Mike Boyle.)
Exercises: MU 6.16, 6.18, 7.1, 7.6, 7.8, 7.13, 7.17, 7.19, 7.26.
Also the following two exercises:
(A) Let the
van der Waerden
function
W
(
k
)
, for nonnegative integer
k
, be the least nonnegative integer
n
so that if
{
1
, . . . , n
}
is twocolored, there exists a monochromatic arithmetic progression with
k
terms. Remarkably,
W
(
k
)
is ±nite for all
k
; the upper bound is immense and the true value is far
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This note was uploaded on 01/05/2012 for the course CS 150 taught by Professor List during the Fall '10 term at Caltech.
 Fall '10
 list
 Algorithms

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