Fe P - Ei Iq . > o } - Eitan .co } N' : Eai 's } F={LInPlu( N' I - - PDF document

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Fe P - Ei Iq . > o } - Eitan .co } N' : Eai 's } F={LInPlu( N' I - - PDF document

Jul 13, 2023 342 likes •432 views

b - an ai FO - b ) h A , - - IE Cn ] P a - . LITTLEWOOD - OFFORD PROBLEM r I rn . P 4936 < s A ERDE 's PAUL : special Case All ai > O : F - { I l za : - b ) En ) c' EI Spenner Fe P - Ei Iq . > o } - Eitan .co } N' :

slide-1
SLIDE 1

A ,

  • an

b

ai FO

IE Cn] P

a

.
  • b)h¥

LITTLEWOOD -

OFFORD PROBLEM

r I 4936

P

< s

.¥

rn PAUL

ERDE

's

:

A

special Case

:

All

ai > O

F - { I l

za: - b)

c' EI

En)

Spenner

Fe

P - Ei Iq

. > o}

N'

  • Eitan.co}

→ F={LInPlu(N'I> II

: Eai 's}

✓ Sterner

slide-2
SLIDE 2

3.53

STRONGLY NEG

CORREIA

,

. . . Am

ER

events

PCA =L

Plain Aj)E¥

⇒

ME 6

  • Xi

:

ind Ii

y = [Xi

Var (4) 20

Uarcy)=§Var(kilt

rlxixjl

itj

slide-3
SLIDE 3

I

permutation

÷ Cn] → In)

bijection

→ t IT; ¥

. !

Chief 4

↳o >

O

  • Period

p ( i. it) = length of cycle

3- i

p (4) =3

p (5) = I

  • P ( per

=k) = 's

←

  • III = n !

T

= set of linear

  • rderings of

Cn]

Pfk

) 31524

TlH,),._#

Tgi ) : j EC

in order

cadet

, 4.171535566

IT

(

→ code Cut by:

P ( merch

= k ) =P ( I

= codeCH , ) =L

slide-4
SLIDE 4

(4

Xlt)= # cycles of IT

Elxlnlnn

EH)= lttzttt.r.tt - Hn

¥

£

↳

harmonic number

'

ICE

FEE

's

's

÷

.

. . .

→ Yi :=¥,

X - EY

,

n

ELX )=EEL%

. )

E( Yi)=¥

,

( perlis -k ) =L Et

T N

kik

babe I

l

l

per

  • h

EU):&

.,÷Hn=Hh

slide-5
SLIDE 5
  • 3. 57

FFEN

:# fixed.pt

  • free

even

permutations

  • f Cn]

FFON :

. .
  • odd
.

.

.

FFEN - FFON

= det (J -I)

  • l ?

=u5'cm, a'- oiiidsmt

.

sign

: {

if

a- I

FFEEFFO,

C- ya

  • l
  • det =§sgaCHtTa

Ling

DE fever

.

L

fears Ir

::3 ? I

i

in

ace to

slide-6
SLIDE 6

Counting spanning trees

in

a graph

: def

Kirchhoff

1848

resistance electrical

circuit

I

⇐ Hell =p

,n

set of

nxu matrices

B t Ma ( Fz )

{ o

,

. . . , p - B

# ( 1343=0

) 22h42

B

  • Kei

"

Izak

(BTB )

= bi

  • bj

=L cig

.

so

i

ith ed

slide-7
SLIDE 7

2nd

solution

,

I totally isotropic subspace 0

  • f drink

in

ten

  • i. e . f-x. y EU) ( x. y

= O)

fi

. En] → V

B

: - (fu

.

.

. .

, find

Bt B

  • O

# f

Mtk

@

"912%

I

%

% Bsf

(E]

slide-8
SLIDE 8

MAXIMAL

ODDTOWN CLUB

SYSTEM

( Ac

.

I = add

their Ajk even

Cn]

Case I

n odd

⑧

take

A - Cn]

N

{ A }

maximal

(Bl odd

[ 1131=1 Baal

  • even}

Cased

neng

Are

  • Case 2

n - I

attempt

⑦

Not MAMMAL

n

clubs

. . .