- 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 . 6,6 ) )= × n contraction remove t FEE - -- Pye - E page - PNE - induction on M

c- * for regular r - uniform hypergraph c- * = en r - fractional cover : - = In Tr Yi ' c- * = I Ey , Z - fractional watching 't tdedeg - I = If u Exe t z v * IF IT - * * c- • • DID NOT c- Ema : . L PIR USE r

prog planes , T 2 ¥±f÷÷i÷¥¥ : ✓ =L Xo 0 € a line is a cover - IS I = n (1) covers ⇐ I edges 44 deg 2N T er . u Intl ) . I = ht ¥ = wtf " (3) T Z t * , 7h

Claim T Intl (2) T cover I Pl ITI * x -4T * Wnt , • • • lines v*=T*=ht¥ - I U E- htt - , V Ld c- = T en

⇒ ' plane possibly def prog ⇒ IPKILI - Generalized Tisher inez : Ecn ) . . . Am A , I Ain Aj tf ti Fj > f ( Ail - m E n - If I E Ipt thiel 22 • - # Z Xo dual H

← us AE¥ I #¥; ' it ' II 's I. . " ' ÷ c- * E 2 - I , e #

n . aitg I ÷ : : = h - rt l KY ' - - E C- ' = h - r TAM VIE is . Emmy met # cover AB " ' , . ¥ : ¥ .

Hadamard 's Inez A - Ca . . . . an ) , Al E II Hai " Idet vol equal if arts . Gran - Schmidt or blog .

Eben town families # mex 2 o . - c) n ' HT > 2K . - BIRKHOFF convfpem )

- Ca . . . an ) A - - Ha ill =L WLOG l dit Al - 1 NTS = ( I ' - 7) Fani def At A Xi ZO E Xi = trace = n = dit LATA )= IT Xi det LAT ) . det CA ) = det (A) 2 NTS ITX