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Cayley's Formula (BMC Advanced) - Shared screen with speaker view
espen slettnes
09:32
https://espen.slett.net/BMC_lectures/Cayleys_Formula/2021-02-03.pdf
Frederick Umminger
10:23
Everyone please turn your video on.
espen slettnes
11:31
https://espen.slett.net/BMC_lectures/Cayleys_Formula/2021-02-03.pdf
espen slettnes
11:52
https://espen.slett.net/BMC_lectures/Cayleys_Formula/2021-02-03.pdf
Jayanth Sadhasivan
13:03
yes
nathan barnes
14:42
1
Mingyang Cen
14:54
Connected vertices
nathan barnes
14:55
(1)-(2)
nathan barnes
15:17
3
nathan barnes
15:34
the only 3-tree is a line
nathan barnes
15:44
So we have 3 with each label in the center
nathan barnes
15:55
(the leaves don't matter because you can reflect it)
Mingyang Cen
16:44
16
nathan barnes
16:54
There are 16 trees for n=4, 4 with the triangle and 12 with the line
Mingyang Cen
19:11
120 for the line
Mingyang Cen
19:34
Oh 60
nathan barnes
20:20
5-trees are the square (4 vertices connected to a center) with 5, the line with 60, a Y-shape with 60 (5*4*3)
nathan barnes
23:00
n^(n-3)
Frederick Umminger
23:12
Everyone, please turn your video on.
nathan barnes
23:32
(n-1)!
espen slettnes
24:06
https://espen.slett.net/BMC_lectures/Cayleys_Formula/2021-02-03.pdf
nathan barnes
25:04
RT/T=n, so RT=n*n!
Minhnha Kawamura
27:36
n
Jason Hallsten
27:37
n-1
Jayanth Sadhasivan
28:05
(n-1)!
Mingyang Cen
28:18
n*(n-1)!
nathan barnes
28:31
n!^2
Mingyang Cen
29:24
n
Mingyang Cen
29:29
n-1
Jason Hallsten
30:19
n-1
Mingyang Cen
30:26
n
Mingyang Cen
31:06
n-2
Mingyang Cen
31:47
n-1
Jayanth Sadhasivan
32:02
1,2,3,4
Jayanth Sadhasivan
32:58
2 is a root
nathan barnes
37:15
n-1
Mingyang Cen
38:05
n^(n-1)
nathan barnes
38:19
(n-1)!
nathan barnes
41:21
n!*n(n-1)/2
Jayanth Sadhasivan
41:22
n(n-1)/2
nathan barnes
41:35
n!*n(n-1)
nathan barnes
41:42
oh
nathan barnes
41:45
n!*n^2
nathan barnes
42:02
oh
nathan barnes
42:15
I forgot we were looking for labeled trees
Mingyang Cen
50:05
Why is 2 going to itself?
Mingyang Cen
50:16
oh
nathan barnes
52:04
bijective
nathan barnes
53:13
2,5,8,10,13,14
nathan barnes
53:27
Because they're in cycles
nathan barnes
55:46
So the order on the bottom is the order of the path between the 2 roots
nathan barnes
01:06:09
6?
Minhnha Kawamura
01:06:41
at least 7
nathan barnes
01:06:42
maybe 8
nathan barnes
01:06:46
I have 8 now
Frederick Umminger
01:07:20
Everyone please turn your video back on.
Mingyang Cen
01:13:37
G
Mingyang Cen
01:13:37
\
Mingyang Cen
01:13:40
sorry
Mingyang Cen
01:13:46
G\e
nathan barnes
01:19:02
-1,4,-1,-1,-1
Minhnha Kawamura
01:19:04
all -1
nathan barnes
01:19:23
-1, -1, 2, 0, 0
nathan barnes
01:19:54
0
nathan barnes
01:22:43
94?
Ian McLellan
01:22:59
16?
nathan barnes
01:27:30
add 1 to (i,j)/(j,i) and subtract 1 from (i,i)/(j,j)
Ian McLellan
01:29:49
Alternating adding and subtracting each number in the matrix times the determinant of the matrix without that number's row and column
Jayanth Sadhasivan
01:33:03
2n
Jason Hallsten
01:33:18
n-1
Minhnha Kawamura
01:33:20
n-1
nathan barnes
01:35:23
0
nathan barnes
01:35:32
1
nathan barnes
01:36:08
Remove it
Andrew Sylvester
01:36:31
add it to every otgher row
Ian McLellan
01:37:14
n^(n-1)
Ian McLellan
01:37:19
oh wait no
Ian McLellan
01:37:23
n^(n-2)
Jason Hallsten
01:39:56
3
Jason Hallsten
01:40:11
4
Andrew Sylvester
01:40:13
6
Jason Hallsten
01:42:31
n will be in the final two
Jason Hallsten
01:42:42
it's the largest
nathan barnes
01:45:15
No leaf can ever be written unless it's n
Mingyang Cen
01:52:52
it is a parking function
Mingyang Cen
01:53:17
Spot 3 isn’t taken
Corinne Young
02:11:26
Thank you!!