Permur www.refereo.ro cele m o refere.noue de permure. Fe A o mulme f de elemee, dc A{,, 3,, }. O fuce becv σ:aàa e umee permure ubue de grdul. P:Numrul uuror permurlor de ord ee egl cu!..produul compuere permurlor. Fe σ τ dou permur de cel grd. Pr compuere celor dou permur e elege o ou permure σ oτ :AàA cu prop. σ oτστ. 3.Propre le compuer permurlor. P: Aocve compuer σoτoφσoτoφ, orcre r f σ;τ;φ ε. P: Compuere permurlor u ee comuv σoττoσ P3: Eleme euru σoееoσ orcre r f σ ε е àpermure dec P4: Eleme merzbl σoσσoσе
4.Trpoz. e umee rpoze o permure de form σ, u, cu propree ì : ï í : ï î : ¹, Propre: P: σ² e P: σ σ P3: σ σ Numrul uuror rpozlor de ord ee egl cu C². Numrul uuror rpozlor de ord ee egl cu umrul perechlor, cu propree c <<. 5.Iverule ue permur. e umee verue ro permure σ o pereche de elemee, < cu propree c σ σ. Numrul verulor ro permure e oez cu Mσ < C². 6.gur ue permur. Fe σε. Numrul σ permur σ. e umee gur emul M e e σ dc Mσ ee pr dc Mσ ee mpr
σ e umee permure pr dc re u umr pr de veru. σ e umee permure mpr dc re u umr mpr de veru. Teorem. Orce rpoze ee o permure mpr. Teorem. Dc σ ε uc e σ Π σ σ /. Teorem 3. Dc σ,τ ε uc e σoτ e σ o e τ. Teorem 4. Dc σ ε ee o permure uc σ poe f decompu c produ de rpoz. Ob: Dc σ ee pr e poe f decompu c produ pr de rpoz dc ee mpr e poe f decompu c produ mpr de rpoz. Aplc.. Fe permurle σ 3 4 τ 3 4. e clculeze 4 3 4 3 σoτ τoσ. σoτ 3 4 τoσ 3 4 3 4 3 4. e deerme umrul de veru gur peru fecre dre permurle urmore:
3 3 Mσ e σ 3 4 4 3 Mσ3 e σ 3 4 4 3 Mσ 3 e σ 3 4 5 5 3 4 Mσ 8 e σ 3. Fe permure σ 3 4 5. e cre σ c produ de 3 5 4 rpoz. Acee problem peru permure τ 3 4 5 6. 6 4 5 3 4,5oσ 3 4 5 o 3 4 5 3 4 5 σ 3 5 4 3 5 4 3 4 5,3oσ 3 4 5 o 3 4 5 3 4 5 σ 3 4 5 3 4 5 3 4 5,3oσ 3 4 5 o 3 4 5 3 4 5 e 3 4 5 3 4 5 3 4 5 ð σ 4,5o,3o,3,6oτ 3 4 5 6 o 3 4 5 6 3 4 5 6 τ 6 3 4 5 6 4 5 3 4 5 3 6,5oτ 3 4 5 6 o 3 4 5 6 3 4 5 6 τ
5 3 4 6 4 5 3 6 4 3 5 6 3,4oτ 3 4 5 6 o 3 4 5 6 3 4 5 6 τ3 4 3 5 6 4 3 5 6 3 4 5 6,3oτ3 e ð τ,6o,5o3,4o,3. 4. Fe permure σε σ 3 4 3 5 7 4. e deerme umrul verulor permur σ. e deerme fel c σ fe pr repecv mpr. e e 4 e 4 e / / 4 4 / / 4 e 4 3 e 44 / 4 4 / 4 4 / 3 Mσ3 / 5. e deerme umrul verulor permur σ. 34. 3 468.. 3. 5..
Mσ34 / 6. Deerm σε 7 fel c 34567 34567 34567 o o 73654 37456 53647 o o 3 o o o o 3 o o 3 3 o o 34567 34567 34567 o o 43765 53647 35674 34567 46735 7. Rezolv 5 ecu: σoxxoσ σ 3 4 5 3 5 4 X 3 4 5 b c d e Xoσ 3 4 5 o 3 4 5 3 4 5 b c d e 3 5 4 b c e d σox 3 4 5 o 3 4 5 3 4 5 σ b 3 5 4 b c d e σ σb σc σd σe
σb c σc σd e σe d d,e ε {4,5} CAZUL I: d4 e5 σ b σb c σc σ b dr σ b σc X 3 4 5 3 4 5 σb c σ c dr σ 3 c3 σ b dr σ 3 b3 σc X 3 4 5 3 4 5 σb c σ3 c dr σ3 c 3 σ3 b dr σ3 b X3 3 4 5 3 4 5 CAZUL II: d5 e4 X4 3 4 5 3 5 4 σb c σ c dr σ c
X5 3 4 5 3 5 4 3 X6 3 4 5 3 5 4. 8. Fe permure u 3 4. e re c u ex c o 3 4 permure X ε 4, fel c X² u. ƐX² Ɛu u ex X. 9. Fe permure σ 3 4 5 6. e deerme fel 6 4 3 c σ fe o permure pr repecv mpr. u 5 5 5 e σ permure ee mpr 5 e σ permure ee pr.. e du umerele rele rc pozve << <. å Peru ce permure σε um ee mxm. Fe τ σo, 3.... 3 3.. 3..
. e du umerele rele rc pozve << <. Peru ce permure σε produul r e u dou umere urle. τσo, å å å å å rm.. e? mx.. m ee r P Õ
. Peru ce permure σε um Õ r P 3 3 3 3..................... Arm P P Õ Õ r r r r r r. e r r r r r r <
ee mm? Fe τ σo, å 3. 3 3 3....... å
3. e du umerele rele << <. Peru ce permurre σε um ee mxm? å å å å rm.. e 3........... å
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