HOMEWORK #1 - MATH 4160
ASSIGNED: SEPT 20, 2016 DUE: THURSDAY OCT 2, 2014
Write your homework solutions neatly and clearly. Provide full explanations and justify all of your
answers.
Stirling numbers and
(1) In class, we dened for k > 0, (x)k := x(x 1)(x
HOMEWORK #4 - MATH 4160
ASSIGNED: MONDAY NOVEMBER 17, 2014
DUE: NOVEMBER 27, 2014
Write your homework solutions neatly and clearly. Provide full explanations and justify all of your
answers.
(1) For each of the following three trees (they are called trees
HOMEWORK #2 - MATH 4160
ASSIGNED: OCT 9, 2014 DUE: OCT 21, 2014
Write your homework solutions neatly and clearly. Provide full explanations and justify all of your
answers.
(1) Use the following diagram to arrive at a binomial formula involving paths in a
NOTES FROM THE FIRST CLASS
MIKE ZABROCKI - SEPTEMBER 9, 2014
The course web page and description is at
http:/garsia.math.yorku.ca/ zabrocki/math4160f14/
The rst thing I did was try to explain what combinatorics is about and what we will
learn in this clas
FOURTH LECTURE : SEPTEMBER 18, 2014
MIKE ZABROCKI
I started o by listing the building block numbers that we have already seen and their
combinatorial interpretations.
S(n, k) = the number of set partitions of cfw_1, 2, . . . , n into k parts
B(n) = the nu
NOTES FROM THE SECOND CLASS
MIKE ZABROCKI - SEPTEMBER 11, 2014
In the rst class we discussed three tools. Let me restate them again here (in a more
general form).
(1) the equality principle:
If there is a bijection between a nite set A and a nite set B, t
FIFTH LECTURE : SEPTEMBER 23, 2014
MIKE ZABROCKI
I put up four identities that I discussed in previous lectures
n
n
(1)nk S(n, k)(x)(k)
x =
k=1
n
xn =
S(n, k)(x)k
k=1
n
(n)
(x)
s (n, k)xk
=
k=1
n
(1)nk s (n, k)xk
(x)(n) =
k=1
We will use only the rst one
NOTES FROM THE FIRST TWO CLASSES
MIKE ZABROCKI - SEPTEMBER 6 & 11, 2012
main idea of this class
1 + 2 + 3 + + n = n(n + 1)/2
to
1r + 2r + + nr =?
Just to show what we are up against:
2
1 + 2 + 3 + + n = n(n + 1)/2
2
1 + 2 + 32 + + n2 = n(n + 1)(2n + 1)/6