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Combinatorics June 30 Chat
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AvatarGreg Miller
7:31
Yes.  the empty set is a subset of every set.
*** Wednesday, July 1 ***
Dayna
10:02
#5 on page 121. Is the empty set a subset of every set?  If so, I think I’m starting to understand.
AvatarGreg Miller
8:34
I'll be honest.. I'm not sure I've wrapped my head fully around 11 and 12 in that section.  I'd need to put pencil to paper.. I'll try and advise on those after I've truly sat and thought on them.. they aren't familiar to me.  Sorry.
8:33
Cadey... on 7... neither.. it's just a problem of interpreting the words of the problem.. "today's change" is An - An-1 and yesterday's change is An-1 - An-2...
8:29
Sabra.. at 5:30.. each time you introduce a new circle into the mix.. it cuts the other circles in a total of 2(n-1) places... and each one of those cuts is responsible for another partition piece appearing.
Cadey
6:10
I am lost on number 7. Are we starting from the beginning or the end?
Sabra
6:05
oops I meant to say number 11 not five
5:35
and then number 12 on pg 122 i feel like this is a partition problem like example 8 but i am not sure
5:32
I am not real sure where to begin on number five from pg 122
5:30
On number one from pg 121 I understand where An-1 comes from put the part throwing me off is the 2(n-1)
AvatarGreg Miller
3:42
This 10 cases respectively give the following generating functions (remember there is a "2" in front of x2):  z(z^4)^2, z(z^3)^2, z(z^2)^2, z(z^2), (z^2)(z^2), (z^2)(z^2)^2, (z^2)(z^2)^3, (z^3)(z^2), (z^3)(z^2)^2, (z^4)(z)^2... when these 10 terms are individually written out they are z^9, z^7, z^5, z^3, z^4, z^6, z^8, z^5, z^7 and z^6... they all belong to 10 mutually exclusive situations, so their contribution to the overall generating function is therefore z^9 + z^8 + 2z^7 + 2z^6 + 2z^5 + z^4 + z^3.
3:37
Regarding the condition x1+x2<6:  this creates the possibilities (1,4), (1,3), (1,2), (1,1), (2,1), (2,2), (2,3), (3,1), (3,2) and (4,1) for those two variables.
3:36
Circling back around to #5 on Five Review Exercises in Section 29 from last night.. first notice the typo in the back that should read "coefficient on z^28, not z^10
3:24
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