- binomial inequality Pure In linear inequality or logs - log Xo - - PDF document

Tropicalizatiou

Geometry

and Extremal

Gurbiuatorics

( Or

How I learned not to

worry

and

love

the tropics )

Joint

with

• A

• F . Rincon , R

Se RI

closed all polynomial

inequalities valid

• u S

Xd z XB

xd * X Bz o

• Pure

binomial inequality

In

linear inequality

• r logs

Ye

• log Xo

{ Lilli 2 E Bi Yi { (Li

• pity,

Zo

S →

logos)

6nelh.gl#)

• right object

4

to study

convex Gue

• sets

with

Hadamard Property

④ ,

• - Hu) * Hi,
• int
• High
• -sxuyu)

x,yes

⇒ x * yes

If

S

has Hadamard property

then ago) = tropes)

• trop est Liya logics )

If

S

is

semi algebraic ⇒

tropes)

a rational

polyhedral complex

IAlessandrini )

A

• - , Lu}

Y

The

following preserve Hadamard property (1)

Monomial

weeps

(2)

Convex

• r comical lull
• A , B Eo

PSD symmetric wonder

A-* B ko

Schur product

Hun

V

• i UVT

bae (out)

lone g PSD

matrices

tropes:)

J

(

'

Yi:)

xoxo

• Xiao

Xu Xu

Xu

Yoo -141, -241020

Also true

if

mom

filled

Ulman urials

• r

pure

binomials

A

Pnf

• polynomial will

support n A wowuegshte

• n khz o

Pat

• NTA

Record

wounds

• n

measures

supported

• n Rko

at =

( SH

be htt . . Lay

NTA

• _

env (yakked)

YA :X Hkd 's . > Xdk)

drop Ctf ) ?3HnkH9o)

+ flirt

10,0)

( 1,21

f-¥

( 2,17

Moha 's Moo

• Uh ,
• Miz

( 111)

Moo - SS da

Unified

Mine SXN-ndfemi-fxx.de

then :

hoop (UTA)

the

• ne

Of

convex

punch bars

• n A

{ *

k

• Sos t

Etf

• will

also have

Hardwood properly

trop LEE)

thus ( it is all g lattice

p b

g

trop (Ej) = puncheon

• r A

hat

are midpoint

convex

• al

I

I Hah

SCH = #

Eg G

D (G)

Can I

# triangles n C

F)

# of

how I → G

• n -

D

u,y O - 9312

19

"

¥4graph

pmfile

Razbiov

S

• Hadamard property

U a collection

g ↳ invoked

graph

tropes)

• appear

to be

a

rational polyhedral

6hL