Kuwerengetsa zonse zitheka. mfundo za combinatorics

chipangizo mu dziko kumapereka lingaliro la kukhalapo kwa yaikulu zosiyanasiyana zochitika ndi zinthu. Pa nthawi yomweyo sayansi wosonyeza kuti maziko a zounjikika izi ndi ya nambala inayake zigawo zikuluzikulu. Kulumikiza mu dongosolo losiyana, midadada awa ndi maziko a zomangamanga mapulani a m'dzikoli. Kuphunzira chiwerengero cha mitundu n'kotheka wa osakaniza zigawo zosiyanasiyana nawo masamu, makamaka gawo lake lotchedwa combinatorics.

Choncho, ngati zinthu kuphunzira mfundo apawokha anavomereza, ndi kuchuluka (permutations, ma, kutengerapo ndi mayikidwe a nyengo) ndi maganizo pa iwo (optionally tsankho dongosolo). zinthu combinatorics ndi wogwirizana kwambiri ndi Masamu ndi ajebura, iwo pafupifupi inakhala maziko a kuwerengetsera mchiphunzitso cha Mwina. Lonse osiyanasiyana minda zosiyanasiyana kudziwa sikutheka kulingalira popanda munda wa sayansi. Nthambi yotchuka kwambiri ya masamu zimene zinayamba mu sayansi zowerengera, chibadwa ndi sayansi kompyuta.

Ndipo chiyambi cha mawu ake, "combinatorial" kuchotsera 1666. Ntchito zake "Nkhani pa luso combinatorial" masamu Leibniz maziko kwa pofuna kukwaniritsa nthambi izi wa masamu.

Nthawi zambiri, kugwiritsa ntchito mawu akuti "combinatorics", kutenga nkhani mbali zambiri onse a apawokha masamu, womwenso Mwachitsanzo, chiphunzitso cha chintchito.

Zochitika za combinatorics nthawi zambiri monga chitsanzo cha masanjidwe combinatorial. Malawi, rearrangement, kuphatikiza, zikuchokera ndi kugawa manambala ndi Gawo, zimene zimapezeka mu chimake cha mfundo za nthambi izi wa masamu.

Malo - anatilamula ya nambala inayake cha zigawo za thupi amaika, ndi nambala bwino chikhalire wa zinthu. Permutation otchedwa mosamalitsa analamula ya nambala lokhazikika la zinthu. Combinatorics kuphatikiza - m'ndandanda wa anatengedwa chiwerengero cha zinthu m'gulu deta. Akanema kusiyana kokha mwa dongosolo la zinthu, koma dongosolo chomwecho, izi ndi kusiyana pakati pa mitundu ndi mayikidwe. chiwerengero cha ma zimadalira kukula kwa zoikika ndi chiwerengero cha zinthu kupanga achikhalire, amene atengedwa kwa yokonza anati combinatorial chitsanzo.

Poganizira mfundo zikuchokera, izo zonse monga chifaniziro cha kuchuluka analamula ku integers positive. Koma kugawa wa - ndi lingaliro lililonse mmene ndalama wake disordered wa integers positive.

Zochitika za combinatorics ankagwiritsa ntchito zosiyanasiyana chidziwitso. Pa nthawi yomweyo iye amachita gawo ili la masamu linakhazikitsa chitukuko sewero chotero amene anathandiza anapeza katundu zambiri mu munda kuonetsetsa partitions.

Poganizira malangizo Chigawo chakuti "Combinatorial enumeration" (quantifiable), kutenga nkhani kulanda kapena aŵerenga masanjidwe kotheka (mwachitsanzo, permutations), amene anapanga ku zinthu kukukhala amalire. Ndi zotheka imposition cha zoletsa zina. Zikuphatikizapo invisibility kapena zinthu akuoneka, kubwereza Maganizo a zinthu zomwezo, ndi zina zotero.

Kuti awerengere nambala ya masanjidwe, ntchito malamulo chakale cha Kuwonjezera ndi kuchulukitsa. Zochitika za combinatorics mu gawo limeneli chilango ntchito pothetsa osiyanasiyana ntchito zosiyanasiyana.

The combinatorics structural anawonjezera nkhani zosiyanasiyana chiphunzitso Zithunzi, chimasonyeza ndi chiphunzitso cha matroids. Mwa zigawo mwambo anatsindika combinatorics kwambiri, Ramsey Akuti Mwina, mtunda, combinatorics infinitary.