MATH 681
Problem Set #5
This problem set is due at the beginning of class on
November 10
.
1.
(5 points)
Find an asymptotically accurate approximation for
(
n
2
n
)
in terms of poly
nomials, exponentials, and selfexponentials. You may write it in bigO notation if you
wish.
2.
(10 points)
You have a large supply of beads of 4 diﬀerent colors and want to string
eight of them on a necklace,
making use of each bead at least once
. How many ways are
there to do so, if necklaces are considered identical if they are rotations or reﬂections
of each other?
3.
(25 points)
Answer the following questions about icosohedroncoloring. You may ﬁnd
it useful to assemble the model at
http://www.korthalsaltes.com/model.php?name_en=icosahedron
in order to help
your visualization.
(a)
(5 points)
Identify the 60 rotationpermutations of the icosohedron. You need
not explicitly give all 60; merely give a classiﬁcation scheme which identiﬁes 60
diﬀerent rotations.
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This note was uploaded on 01/12/2012 for the course MATH 681 taught by Professor Wildstrom during the Fall '09 term at University of Louisville.
 Fall '09
 WILDSTROM
 Approximation

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