This preview shows page 1. Sign up to view the full content.
MATH 239 Assignment 3
This assignment is due at noon on Friday, June 8, 2007, in the drop boxes opposite the Tutorial
Centre, MC 4067.
1. (a) Determine a generating function for the compositions of
n
in which all parts are odd.
As usual, the weight of a composition is the sum of its parts.
(b) Determine a generating function for the of compositions of
n
in which at least one part
is even.
(c) Let the number of compositions of
n
with at least one even part be
b
n
. Determine a
recurrence relation for the
b
n
’s, and suﬃcient initial conditions to uniquely deﬁne the
terms of the sequence
{
b
n
}
. Evaluate
b
10
.
2. (a) Let
A
=
{
10
,
101
}
and let
B
=
{
001
,
100
,
1001
}
. For each of the sets
AB
and
BA
, de
termine whether or not the elements are uniquely created. Find the generating function
for
AB
and
BA
with respect to length.
(b) Let
A
=
{
00
,
101
,
11
}
and
B
=
{
00
,
001
,
10
,
110
}
. Prove that the elements of
A
*
are
uniquely created, but the strings of
B
*
are not. Find the generating function for
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '09
 M.PEI
 Math

Click to edit the document details