Slide Set 034: Generating Functions and their Delightful Applications to Random Networks
We absorb the dark powers of Generatingfunctionomancy.
Reheated slides on toast:
47M
; Last updated: 2023/08/22, 11:48:23
Freeze-dried snack slides:
1.4M
; Last updated: 2023/08/22, 11:48:21
Original slides as served in lectures:
48M
; Last updated: 2023/08/22, 11:48:25
Covered in these episode(s) and clip(s):
Clip 1: The Dark Art of Generatingfunctionomancy (12:42)
Clip 2: Generating functions: Example calculations (3:43)
Clip 3: Generating functions: Computing the average degree (4:27)
Clip 4: Generating functions: Higher moments and more (4:09)
Clip 5: Generting function recap (3:04)
Clip 6: Inversion formula for probability generating functions (9:07)
Clip 7: Generating function deliciousness for sums of variables (1:55)
Clip 8: Giant component condition, generatingfunctionally (16:48)
Clip 9: Component size distributions (4:27)
Clip 10: Recursion story with pictures (13:01)
Clip 11: Sneaky generating function story for random sums of randomness (16:59)
Clip 12: Generating function refresh (6:22)
Clip 13: Simple V = U + 1 generating function rule (3:01)
Clip 14: Recursive equations for finite component size p.g.f.'s (11:32)
Clip 15: Giant component size calculation (3:41)
Clip 16: Component size distributions for standard random graphs (14:55)
Clip 17: A very pleasing simple network calculation (25:47)
Clip 18: Finding finite component size distributions with generating functions (6:47)
Clip 19: Distribution of finite component sizes: Standard random networks (7:50)
Clip 20: Distribution of finite component sizes: Simple mixed network (5:58)