Combinatorics
Professor Imre Leader
2. Chapter II: Isopermietric inequalities
How tightly can we pack a set of given size?
For example, among subsets of R2 of given area, the disc has the smallest perimeter. Similarly
in R3 .
Im supposed to ramble about s
Combinatorics
Professor Imre Leader
Course overview
This course will be organized in three chapters:
1. Set systems: a simple combinatorial setting (subsets of the powerset of a finite set) where
interesting structure emerges;
2. Isoperimetric inequalitie
Combinatorics: Problem set 2
1. Problem 1
Observe that if i(A) indicates the size of the largest intersecting family contained in a set
system A, we have
X
i(X (r) )
i(X (j) )
jr
(r)
because if A X
is intersecting, so is every slice A X (j) . But the Erd
Combinatorics: Problem set 1
Professor Imre Leader
1. Problem 4
Remember the matchings we constructed in class between X (r) and X (r+1) by Halls theorem!
We can use these here to push our set system to the middle two layers.
More formally, among all set
Combinatorics
Professor Imre Leader
3. Chapter III: intersecting families
Say A P(X) is t-intersecting if |x y| t for all x, y A. How large can a t-intersecting
family be?
n
For t = 2, could take x 1, 2 x of size 24 . But! We can beat it by taking all
Hypergraphs
Professor Andrew Thomason
We defined ex(n, F ) and (F ) for hypergraphs. Let Krl be the complete l-uniform hypergraph
on r vertices. No value of (Krl ) is known for r > l 3.
Tur
an conjectured that (K43 ) = 5/9. Erdos offered $5000 in his memo
Extremal graph theory
Professor Andrew Thomason
2. Chapter II. Stability
An extremal problem is stable if every near-optimal (that is, having almost ex() edges)
example is very close to some specific extremal graph. [Intuition: we can think of that as say
EXTREMAL GRAPH THEORY
PROFESSOR ANDREW THOMASON
dis regularity lemma
3. Chapter 3. Szemere
Its cool because it tells us something about the structure of every graph, and has very useful
applications to e.g. arithmetic number theory.
A graph with the (larg
Extremal graph theory
Professor Andrew Thomason
4. Chapter 4: Containers
We consider r-uniform hypergraphs G of order N and average degree d (typically we need d
large to get useful results).
So each edge is a subset of the vertex set of size r. The degre
EXTREMAL GRAPH THEORY
PROFESSOR ANDREW THOMASON
s-Stone theorem
1. Chapter 1. The Erdo
1.1. Tur
ans theorem. We begin with a basic result from extremal graph theory that will be
the basis for much generalization.
Theorem 1.1 (Tur
ans theorem, also due to
GLOBAL PRIVATE EQUITY REPORT 2016
About Bain & Companys Private Equity business
Bain & Company is the leading consulting partner to the private equity (PE) industry and its stakeholders. PE
consulting at Bain has grown vefold over the past 15 years and no
Search Criteria: Fund Type: Buyout; Fund Vintage Year: From: 2010; Fund Location: Europe > Northern Europe;
Fund ID
Fund Name
Fund Former Name
PBId
13589-83F
CapMan Buyout X
13589-
12184-21F
CapMan Buyout IX
12184-
13677-40F
EQT VII
13677-
13638-07F
EQT M
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This workbook contains the corresponding charts and tables
V
GBP
10/30/2014
3
4
Company name
Crncy
Share Price
EQY_FUND_CRNCY
EQY_FUND_YEAR
BEST_FPERIOD_OVERRIDE
Ticker
Ctry
COUNTRY_FULL_NAME
LONG_COMP_NAME
TNB MK EQUITY
MALAYSIA Tenaga Nasional Bhd
YTLP MK EQUITY
MALAYSIA YTL Power International Bhd
MLK MK EQUITY
Fixed Asset and Depreciation Schedule: Instructions
This worksheet is intended to assist in tracking an organization's fixed assets and annual depreciation estimates.
Note: the template assumes that all assets are depreciated on a straight-line basis. For
XNPV
Warning: XNPV will not discount the first cash flow you point it to (irrespective of the date attached to that cash flow).
In other words, XNPV assumes that the first cash flow happens today, regardless of whether you have attached a date to it.
If y
Compound interest formula
Tells us how much money we will have tomorrow, given interest rate and time
Money in
Time (years)
Rate (1%)
Money out
20.0
5
1%
21.0
Discounting in Excel
Tells us how much money tomorrow is worth to us today
Money out
Time (years