Веленкин;Комбинаторика
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zjrvmv xwvxvij nxz• &Q−S |
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& & |
+ & & |
+ + &P &P |
= &P |
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S P |
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-sjkj ,, и¬dОcХcЛК‰ НcиcfТ¬ЛМЖЗК К fМпcТ¬ЛК‰
Æ·jxztvxzq wéq S = P qunnu éjkntxzkv
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Æ {véuysn k rj lvu xsjmjnuvu xyuuj kné}tq} |
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qtlnrxvk éjktj P j |
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tqn qtlnrx€ |
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tyí {véuysy k rvzvévp wéq xyuuqévkjtqq unt¹ízx¹ tq tqn |
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qtlnrx€ j kné}tqn wvxzv¹tt€ |
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·qxsv xv·nzjtqp k}vl¹•q} k N p rsjxx
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Ínénwq¡nu ëzv zv lnxzkv zjr ·zvi€ wéq xyuuqévkjtqq
unt¹sqx• sq¡• tq tqn qtlnrx€ bs¹ ëzvmv tjlv rv kxnu |
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êzy {véuysy uv tv qtj·n wnénwqxjz• xsnlyí•qu viéjovu oj untqk S tj S + Q tj Q + q P tj P − Q
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+ &S |
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΀ kqlqu ·zv olnx• wéq xyuuqévkjtqq kné}tqn qtlnrx€ vxzjízx¹ wvxzv¹tt€uq j tq tqn unt¹ízx¹ wéq·nu xyuuj kné}tq} qtlnrxvk éjktj Q j tq tq} P
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Ívsy·ntt€n zv lnxzkj uv tv vivi•qz• bs¹ ëzvmv éjxxuvzéqu xvkvrywtvxz• xvxzv¹•yí qo ësnuntzvk T zqwvk Q ësnuntzvk wnékvmv
zqwj Q ësnuntzvk kzvévmv zqwj QT ësnuntzvk T mv zqwj wéq·nu
ësnuntz€ vltvmv zqwj vzsq·t€ léym vz léymj tjwéquné zqw ² ëzv |knz wénlunzj tv éjot€n wénlunz€ vltvmv |knzj quníz n•n éjosq· tyí {véuy Èylnu xvxzjks¹z• qo ësnuntzvk ëzvp xvkvrywtvxzq kxn kvouv t€n xv·nzjtq¹ ino wvkzvéntqp wv P ësnuntzvk q rsjxxq{q|q évkjz• q} wv xvxzjky z n wv ·qxsy ësnuntzvk wnékvmv kzvévmv
T mv zqwvk Òjrqu viéjovu rj l€p rsjxx }jéjrznéqoynzx¹ tjivévu tjzyéjs•t€} ·qxns P P PT ylvksnzkvé¹í•q} tnéjkntxzkju
≤ PL ≤ QL wéq·nu P + P + + PT = P Ìt xvxzvqz qo P ësnuntzvk wnékvmv zqwj P ësnuntzvk kzvévmv zqwj PT ësnuntzvk T mv zqwj
΀ iylnu vivotj·jz• zjrvp rsjxx $(P PT)
Êo wéjkqsj wévqoknlntq¹ k€znrjnz ·zv k rsjxx $(P PT) k}v
lqz &P &P &PT xv·nzjtqp fyuuqéy¹ ·qxsj xv·nzjtqp wv kxnu rsjx |
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c•n vltv xkvpxzkv xv·nzjtqp yxzjtjksqkjnzx¹ zjr ΀ qunnu zv lnxzkv
N P−N = &N &P |
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êzv zv lnxzkv snmrv wévkné¹nzx¹ tnwvxénlxzknttv tv uv tv wév knxzq q rvuiqtjzvétvn éjxxy lntqn bs¹ ëzvmv éjxxuvzéqu xsnlyí•yí
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N ësnuntzvk qo Q j ojznu P − N qo vxzjk¡q}x¹ Q − N ësnuntzvk wv
sy·qzx¹ snkj¹ ·jxz• {véuys€ ¬ uv tv xtj·jsj k€iéjz• P ësn untzvk qo Q j ojznu xénlq ëzq} P ësnuntzvk k€iéjz• N k wnékvn
-sjkj ,, и¬dОcХcЛК‰ НcиcfТ¬ЛМЖЗК К fМпcТ¬ЛК‰
xv·nzjtqn vxzjk¡qnx¹ ljlyz kzvévn xv·nzjtqn xvlné j•nn P − N ësn untzvk wvsy·qzx¹ wéjkj¹ ·jxz• {véuys€
djwq¡nu zv lnxzkv wéq N = P q xsv qu wvsy·qk¡qnx¹ éjkntxzkj Òjr rjr wv {véuysn
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qzn ·zv (&U+ − &U)&U− = |
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mln xyuuqévkjtqn éjxwévxzéjtntv tj kxn |ns€n tnvzéq|jzns•t€n én ¡ntq¹ yéjktntq¹ N + N + + PNP = P
Êxwvs•oy¹ {véuysy
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k€·qxsqzn xsnlyí•qn xyuu€
j & + & + & + & + + Q&Q
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k & + & + & + & + + (Q − )&Q
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m & + & + & + & + + ( Q + )&Q
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l & − & + & − & + + (− )Q(Q + )&Q
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xvxzvqz qo ·qxns êsnuntz€ rj lvp xsnlyí•np xzévrq ¹ks¹ízx¹ xyuujuq ësnuntzvk wénl€ly•np xzévrq xzv¹•q} xsnkj q xwéjkj vz ljttvmv ·qxsj bvrj qzn ·zv ësnuntz wvxsnltnp xzévrq zénymvs•tqrj lnsqzx¹ tj
ïjxzt€p xsy·jp {véuys€ krsí·ntqp q qxrsí·ntqp
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ljí•q} xkvpxzkjuq D DQ ojkqxqz tn vz xjuq} ëzq}
xkvpxzk j sq¡• vz rvsq·nxzkj vltvkénunttv k€wvst¹nu€} xkvpxzk z n
1 = 1 ·qxsv kxn} ësnuntzvk
1(D ) = 1(D ) = = 1(DQ) = 1
1(D D ) = 1(D D ) = = 1(D DN) = 1(D D ) = = 1(DQ− DQ) = 1
1(D D D ) = 1(D D D ) = = 1(DQ− DQ− DQ) = 1
1(D D D DQ) = 1Q
Èylnu x·qzjz• kné}tíí xzév·ry x 1 tysnkvp zvmlj k
wnékvp |
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