- Claim : Pye www.alctf-XCX IT Rb ' - - ( x - KH ) - D 1 IT - - PDF document

claim pye alctf xcx it rb x kh d 1 it partition deg n k
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- Claim : Pye www.alctf-XCX IT Rb ' - - ( x - KH ) - D 1 IT - - PDF document

Chromatic polynomial - ( V , E ) M - eyed f : V - s ti Efx ] VE EE - ' Eff Ci ) - Claim : Pye www.alctf-XCX IT Rb ' - - ( x - KH ) - D 1 IT partition deg = n k classes monic E legal HE 172 illegal Pfe '= pgelxi-pE.cn HE Hi


slide-1
SLIDE 1

Chromatic polynomial M

  • (V

, E )

f : V -

s

eyed

ti Efx] VE EE

Eff

  • '

Ci)

  • Pye

Claim :

IT

'

Rb

www.alctf-XCX

  • D
  • - (x -KH)

1 IT partition

deg = n

k classes

monic

slide-2
SLIDE 2

HE 172

E legal

illegal

Pfe'¥= pgelxi-pE.cn

← → HE

Hi

.

6,6)

contraction

)=×n

remove t FEE

  • page
  • - Pye - E
  • PNE
  • induction on M
slide-3
SLIDE 3

c-* for regular

r-uniform

c-* = en

hypergraph

r

  • fractional

cover:

Yi

'
  • = In

Tr

Ey,

=I

Z

c-*

  • fractional watching

Exe

  • I = If u

't tdedeg

t

  • c-

*

z v * IF IT

*

  • :.

c-Ema

DIDNOT

r

USE

LPIR

slide-4
SLIDE 4

prog planes

2

, T

✓ =L

Xo

0€

¥±f÷÷i÷¥¥:

a line

is

a cover -

(1)

ISI = n

covers

⇐ I

edges 44 2N T

er . u deg

Intl) .I

(3) T Z t *

= wtf

" = ht ¥

, 7h

slide-5
SLIDE 5

Claim

T Intl

(2)

T

cover

ITI *

I Pl

x -4T

*

  • Wnt ,

lines

U

  • I

v*=T*=ht¥

,

E-htt

V Ld

c- = T

en

slide-6
SLIDE 6

possibly def

prog

' plane

⇒ IPKILI

  • Generalized Tisher inez:

A ,

. . . Am

Ecn)

I Ain Ajtf

ti Fj

(Ail

> f

m E n

  • If I E Ipt

thiel 22

  • #

Z

Xo

dual

H

slide-7
SLIDE 7

← us

AE¥

I

#¥;

'II's

I.

'it

.

c-* E 2 - I, e

" '÷

#

slide-8
SLIDE 8

n.aitg

I

÷

::

=h - rt l

  • KY

'

  • E

C- ' = h - r

TAM VIE

is

AB

'

,

. " . Emmy met# cover

¥:

¥

.

slide-9
SLIDE 9

Hadamard 's Inez

A - Ca.

. . . an)

Idet

,Al EII Hai"

vol

equal if

arts

.

Gran -Schmidt orblog

.
slide-10
SLIDE 10

# mex

Ebentown families

  • .
.

2

HT > 2K

  • c) n'
  • BIRKHOFF

convfpem)

slide-11
SLIDE 11

A -

  • Ca.

. . an)

WLOG

  • Haill =L

NTS

lditAl - 1

AtA

= (I

' -7) Fanidef

Xi ZO

E Xi

= trace = n

IT Xi

= dit LATA)=

det LAT)

.det CA)

NTS

= det (A)2

ITX