Xam tag nrho cov tau. ntsiab ntawm combinatorics

ntaus ntawv nyob rau hauv lub ntiaj teb no presupposes lub hav zoov ntawm ib tug lossis loj ntau yam ntawm cov txheej xwm thiab tej khoom. Nyob rau tib lub sij hawm science proves tias lub hauv paus ntawm no abundance yog ib tug txheej ntawm ib tug tej yam muaj pes tsawg tus ntawm Cheebtsam. Txuas nyob rau hauv ib tug txawv kev txiav txim, cov blocks yog lub hauv paus rau lub architectural Siv ntawm lub ntiaj teb no nyob ib ncig ntawm peb. Txoj kev tshawb no ntawm tus xov tooj ntawm tag nrho cov tau variants ntawm ib tug ua ke ntawm cov ntau yam kev koom tes nyob rau hauv kev kawm txog zauv, nyob rau hauv particular nws seem hu ua combinatorics.

Yog li, raws li cov khoom ntawm txoj kev tshawb discrete qhov tseem ceeb txais, ib tug plurality (permutations, ob peb ua ke, hloov thiab kev tso kawm ntawm lub ntsiab) thiab cov xeeb ceem rau lawv (optionally ib nrab txiav txim). combinatorics ntsiab muaj ib tug nyob ze kev twb kev txuas nrog geometry thiab algebra, lawv yuav luag los ua lub hauv paus rau suav nyob rau hauv cov kev tshawb xav ntawm ntau yam. Ntau yam sib txawv ntawm cov teb ntawm kev txawj ntse yog tsis yooj yim sua xav txog tej yam tsis muaj kev siv ntawm daim teb no ntawm science. Cov feem nrov ceg ntawm kev kawm txog zauv uas pib nyob rau hauv statistical physics, noob caj noob ces thiab computer science.

Thiab pib ntawm nws lub sij hawm, "combinatorial" yuav siv sij hawm los ntawm 1666. Nyob rau hauv nws cov hauj lwm "Discourse rau lub combinatorial art" mathematician Leibniz nteg lub lub hauv paus rau lub ntxiv kev loj hlob ntawm no ceg ntawm kev kawm txog zauv.

Heev feem ntau, siv lub sij hawm "combinatorics", noj mus rau hauv tus account ib tug ntau dav seem ntawm discrete lej, uas muaj xws li, piv txwv li, lub hom phiaj ntawm graphs.

Hais ntawm combinatorics yog feem ntau hais raws li ib tug qauv ntawm combinatorial configurations. Kev pab, rearrangement, thaum lawv tseem, muaj pes tsawg leeg thiab muab faib tus xov tooj yog lub ntsiab Cheebtsam, uas yog nyob rau hauv cov embodiment ntawm lub hauv paus ntsiab lus ntawm no ceg ntawm kev kawm txog zauv.

Placement - ib tug kom set ntawm ib tug tej yam muaj pes tsawg tus ntawm Cheebtsam teej tug mus rau ib pawg, nrog ib tug zoo-sau tseg tooj ntawm cov ntsiab. Permutation hu ua nruj me ntsis kom set ntawm ib tug tsau tooj ntawm cov ntsiab. Combinatorics ua ke - ib tug txheej ntawm coj lub xov tooj ntawm cov khoom muaj nyob rau hauv cov ntaub ntawv. Poob lawm yog sib txawv xwb nyob rau hauv qhov kev txiav txim ntawm lub ntsiab, tab sis lawv yog tib cov qauv, qhov no yog qhov txawv ntawm qhov thaum lawv tseem thiab kev tso kawm. Cov nab npawb ntawm cov ob peb ua ke nyob rau hauv lub loj ntawm lub teeb thiab tus naj npawb ntawm cov ntsiab ua li lub teeb, los ntawm uas yog npaum li cas rau qhov kev npaj ntawm hais tias combinatorial qauv.

Xav txog lub tswvyim ntawm nyob tus yeees ntawm, coj nws tag nrho raws li ib tug sawv cev ntawm tus nqi kom los ntawm qhov zoo zauv. Tab sis muab faib rau ntawm - yog ib lub tswv yim yuav ua li cas nws disordered sum ntawm zoo zauv.

Hais ntawm combinatorics yog lug siv nyob rau hauv ntau yam teb ntawm kev txawj ntse. Nyob rau tib lub sij hawm nws ua li no yog ib feem ntawm kev kawm txog zauv dhau xws li ib tug ua txoj kev loj hlob uas tau enabled lub sau hnab nqa taug kev ntaub ntawv nyob rau hauv daim teb no faib partitions.

Xav cov kev qhuab qhia seem cai "combinatorial enumeration" (quantifiable), noj mus rau hauv tus account lub hloov lwm lub tsev los yog suav cov xov tooj uas tau configurations (piv txwv li, permutations), uas yog tsim los ntawm cov ntsiab ntawm cov finite poob lawm. Nws yog ua tau rau hauv lub imposition ntawm tej yam kev txwv. Cov no muaj xws invisibility los yog khees hais, rov hais dua cov kev daws teeb meem ntawm lub tib yam, thiab ntxiv mus.

Yuav kom xam tus naj npawb ntawm configurations, siv lub classical cai ntxiv thiab npaug. Hais ntawm combinatorics nyob rau hauv qhov seem ntawm kev qhuab qhia uas siv los daws tau ib tug ntau ntawm cov ntau yam kev pab raws qib.

Cov yam ntxwv combinatorics ntxiv ib tug xov tooj ntawm tej teeb meem ntawm lub teeb kev tshawb xav, qhia tau hais tias tus ntawm cov kev tshawb xav ntawm matroids. Cov kem ntawm kev qhuab qhia no kuj tseem ceeb huab combinatorics, Ramsey kev tshawb xav, qhov muaj tseeb, topology, combinatorics infinitary.