Combinatorial teeb meem. Qhov yooj yim combinatorial teeb meem. Combinatorial teeb meem: Piv txwv

Cov xib fwb ntawm kev kawm txog zauv paub lawv cov tub ntxhais kawm nrog lub tswvyim ntawm "combinatorial teeb meem" yog tseem nyob rau hauv lub thib tsib qib. Qhov no yog tsim nyog los xyuas kom meej tias lawv twb tau mus ntxiv ua hauj lwm nrog ntau yam dej num. Nyob rau hauv combinatorial teeb meem yuav tau menyuam lub sijhawm los daws nws los ntawm txoj kev tshawb nrhiav cov ntsiab ntawm cov finite teeb.

Lub ntsiab seb mob dab tsi ntawm cov teeb meem ntawm kev txiav txim no yog cov lus nug rau lawv, uas suab zoo li "Yuav ua li cas xaiv?" Los yog "Yuav ua li cas muaj ntau txoj kev?" Combinatorial teeb meem yog nyob ntawm seb los yog tsis tau daws tau lawv lub ntsiab lus to taub, txawm nws muaj peev xwm kom raug sawv cev rau qhov kev txiav txim los yog cov txheej txheem uas tau piav nyob rau hauv txoj hauj lwm.

Yuav ua li cas los daws kom tau ib tug combinatorial teeb meem?

Nws yog ib qho tseem ceeb kom raug txheeb xyuas lub hom tag nrho cov muaj nyob rau kev sib txuas nyob rau hauv qhov teeb meem, tab sis nws yog tsim nyog los xyuas raws li seb nws repeats ntsiab yog lub ntsiab rau lawv tus kheej hloov yog hais tias ib tug luag hauj lwm loj no yog ua si los ntawm lawv cov kev txiav txim, raws li zoo raws li nyob rau lwm yam.

Lub combinatorial teeb meem yuav muaj ib tug xov tooj ntawm cov kev txwv uas yuav raug rau cov compound. Nyob rau hauv cov ntaub ntawv no, koj yuav tsum tau suav tag nrho nws kev txiav txim siab mus xyuas, seb cov kev txwv muaj tej cawv rau cov kev twb kev txuas ntawm tag nrho cov Cheebtsam. Yog hais tias cov nyhuv yog tiag tiag muaj, koj yuav tau xyuas seb dab tsi nws yog.

Pib qhov twg?

Ua ntej peb yuav tsum tau kawm los daws kom tau elementary combinatorial teeb meem. Mastering yooj yim ntaub ntawv pub rau kawm kom paub txog ntau yam dej num. Peb pom zoo kom hais tias koj pib kom daws tau qhov teeb meem nrog xyuas uas tsis tau muab los xav nyob rau hauv ib tug ntau yooj yim kev xaiv.

Nws kuj pom zoo mus sim daws cov teeb meem ua ntej, uas yuav tsum tau raug xam tias yog ib tug me me muaj pes tsawg tus ntawm yam uas hais. Yog li ntawd koj yuav to taub lub hauv paus ntsiab lus ntawm txoj kev kuaj thiab kawm nyob rau hauv lub neej yav tom ntej nyob rau hauv lawv tus kheej mus tsim lawv. Yog hais tias ua hauj lwm rau cov uas yuav tsum tau mus siv combinatorial muaj ib tug ua ke ntawm ob peb sob, nws yog pom zoo kom daws tau nws los ntawm qhov chaw.

combinatorial teeb meem

Tej teeb meem zoo li yooj yooj yim nyob rau hauv qhov kev txiav txim, tab sis cov combinatorics yog heev nyuab los tsim, ib txhia ntawm lawv tsis muaj ib tug daws rau yav dhau los lawm puas xyoo. Ib qho ntawm feem tseem ceeb paub tab yog los mus txiav txim tus naj npawb ntawm cov khawv koob squares ntawm ib tug tshwj xeeb txoj kev nyob rau hauv uas lub xov tooj n yog ntau tshaj 4.

Combinatorial teeb meem yog zoo yam rau cov kev tshawb xav ntawm ntau yam, uas nyob rau hauv medieval lub sij hawm. Qhov ntau yam ntawm keeb kwm ntawm ib tug kev tshwm sim muaj peev xwm yuav xam nrog rau kev siv ntawm combinatorics, nyob rau hauv cov ntaub ntawv no koj yuav tsum tau ua lwm ntawm tag nrho cov ntawm cov yam tseem ceeb nyob rau hauv ib txhia qhov chaw kom tau txais cov kev pom kev tov.

Lub rooj sib tham txoj kev sib tw

Combinatorial teeb meem nrog cov tshuaj siv rau txoj kev kawm ntawm cov menyuam kawm ntawv thiab cov menyuam kawm ntawv ua hauj lwm nrog cov khoom no. Yog hais tias peb tham nyob rau hauv Feem ntau, lawv yuav tsum ua ib tug neeg uas txaus siab thiab txoj kev xav tau ib qho tshuaj. Nyob rau hauv tas li ntawd mus zauv, nws yog tsim nyog los siv cov kev puas hlwb kev nyuaj siab thiab siv ib tug xam.

Nyob rau hauv tus txheej txheem ntawm kev daws cov teeb meem ntawm tus me nyuam yuav muaj peev xwm coj lawv cov tswv yim thiab xaam combinatorial muaj peev xwm, nws muaj peev xwm tiag yuav pab tau kom nws nyob rau hauv lub neej yav tom ntej. Maj mam, lub theem ntawm complexity ntawm cov paub tab uas koj xav tau los txhim kho, tsis txhob hnov qab cov uas twb muaj lawm paub thiab ntxiv mus rau lawv.

Txoj 1. iterate

Txoj kev daws teeb meem combinatorial yog sib txawv heev los ntawm txhua lwm yam, tab sis lawv muaj peev xwm yuav siv tau rau tus menyuam kawm ntawv cov lus teb. Ib tug ntawm cov simplest, tab sis nyob rau tib lub sij hawm thiab tus coos txoj kev mus rau ib tug bust. Thaum nws yog tsim nyog los tsuas sim tau kev daws teeb meem tsis ua tej kos duab thiab cov ntxhuav.

Raws li txoj cai, cov lus nug nyob rau hauv xws li ib tug teeb meem txuam nrog rau cov kev xaiv ntawm keeb kwm ntawm ib tug kev tshwm sim, xws li: dab tsi xov tooj peev xwm yuav tsim nrog cov zauv 2, 4, 8, 9? By sim tag nrho cov kev xaiv kos mus txog ib lub teb uas muaj cov tau ob peb ua ke. Xws li ib tug txoj kev yog zoo tagnrho, yog hais tias lub xov tooj ntawm cov kev xaiv yog tus me me.

2. Cov kev embodiment Ntoo

Ib txhia combinatorial teeb meem yuav tau daws tsuas los ntawm kev ua cov tswvyim, nyob rau hauv cov ntaub ntawv uas hais txog txhua yam khoom yuav tsum tau teev tseg nyob rau hauv kom meej. Yog nqus tau mus ib tsob ntoo cov kev xaiv - lwm txoj kev los nrhiav cov lus teb. Nws yog haum rau kev daws teeb meem tsis nyuaj heev kev pab raws qib, nyob rau hauv uas muaj yog ib tug ntxiv mob.

Ib qho piv txwv ntawm qhov teeb meem no:

• Yuav ua li cas yog tsib zauv peev xwm yuav tsim los ntawm cov lej tom qab 0, 1, 7, 8? Yuav kom daws tau qhov yuav tsum tau los mus tsim ib tsob ntoo ntawm tag nrho cov tau ob peb ua ke, thaum muaj ib tug ntxiv mob - tus xov tooj yuav tsis pib los ntawm kos. Yog li, cov lus teb yuav muaj xws li tag nrho cov zauv uas yuav pib thaum 1, 7 los yog 8.

Tsim txoj kev 3 ntxhuav

Combinatorial teeb meem yuav ua tau los ntawm txoj kev ntxhuav. Lawv yog cov uas zoo sib xws mus rau tsob ntoo ntawm kev xaiv vim hais tias nws muaj ib tug meej tov rau qhov teeb meem no. Yuav nrhiav tau cov lus teb koj yuav tsum tau tsim ib lub rooj, thiab nws yuav tsum mirrored kab rov tav thiab ntsug tej yam kev mob yog tib yam.

Cov lus teb yuav tsum tau ntawm cov kev tshuam ntawm txhua thiab kab. Nyob rau hauv cov ntaub ntawv no, cov lus teb rau cov kev tshuam ntawm kem thiab kab yuav tsis tau txais tib yam cov ntaub ntawv, cov kev tshuam yuav tsum tshwj xeeb cim, tsis yuav tsum tau meej pem nrog nqus up ntawm tus kawg teb. Qhov no yog tsis heev feem ntau xaiv cov thwjtim, ntau xav ib tsob ntoo nrog kev xaiv.

Txoj 4. npaug

Muaj yog ib txoj kev los ntawm cov uas koj yuav kom daws tau combinatorial teeb meem - npaug txoj cai. Nws yog zoo meej nyob rau hauv cov ntaub ntawv, thaum tus mob yog tsis tsim nyog los sau tag nrho cov tau kev daws teeb meem, koj cia li yuav tau mus nrhiav lub siab tshaj plaws pes tsawg tus. Qhov no yog cov tsuas yog ib qho ntawm nws hom, nws yog siv ntau heev, thaum nyuam qhuav pib mus daws tau combinatorial teeb meem.

Ib qho piv txwv ntawm qhov teeb meem no tej zaum yuav raws li nram no:

• 6 tus neeg cia siab tias nyob rau hauv cov tub ntxhais nrog. Yuav ua li cas muaj ntau txoj kev yuav siv tau mus rau qhov chaw lawv nyob rau hauv daim ntawv? Rau Teb yog tsim nyog los qhia kom meej yuav ua li cas muaj ntau yam ntawm lawv tej zaum yuav tau los ua thawj, tab sis nyob rau hauv lub thib ob, thib peb, thiab hais txog. D. Cov lus teb yuav tsum muaj pes tsawg 720.

Combinatorics thiab nws cov hom

Combinatorial teeb meem tsis yog tsuas yog lub tsev kawm ntawv cov ntaub ntawv, lub tsev kawm ntawv cov menyuam kawm ntawv kuj kawm nws. Nyob rau hauv science, muaj ntau ntau hom ntawm combinatorics, thiab txhua tus ntawm lawv muaj nws tus kheej lub hom phiaj. Combinatorial enumeration yuav tsum xav txog cov teeb meem rau hloov lwm lub tsev thiab count tau configurations nrog ntxiv tej yam kev mob.

Lub Khoos Loos Tsev combinatorics yog ib feem ntawm lub tsev kawm ntawv qhov kev pab cuam, nws tshuaj xyuas qhov kev tshawb xav ntawm matroids thiab graphs. Huab combinatorics kuj muaj mus ua nrog high school cov khoom, thiab ntawm no yog lawv ib tug neeg cov kev txwv. Lwm seem - Ramsey kev tshawb xav yog txoj kev tshawb no ntawm cov qauv nyob rau hauv random variations ntawm cov ntsiab. Muaj kuj yog ib tug kwm combinatorics, uas yog xaiv cov compatibility ntawm tej ntsiab ntawm lawv tus kheej.

Txoj kev qhia combinatorial teeb meem

Raws li cov ntaub ntawv kawm, cov hnub nyoog ntawm cov me nyuam kawm ntawv, uas yog tsim los rau thawj zaug acquaintance nrog rau cov khoom thiab daws ib combinatorial teeb meem - 5 chav kawm ntawv. Nws yog muaj rau cov thawj lub sij hawm no lub npe yog muaj rau cov cov menyuam kawm ntawv, lawv tau ntsib nrog rau cov tshwm sim ntawm combinatorial thiab sim daws tau lawv kev pab raws qib. Nws tseem ceeb heev uas cov qauv siv nyob rau hauv lub formulation ntawm ib tug combinatorial teeb meem thaum cov me nyuam yog koom nyob rau hauv kev nrhiav cov lus teb rau cov lus nug.

Ntawm lwm yam, tom qab kev kawm no lub npe yuav yooj yim npaum li yuav ua kom paub lub tswvyim ntawm factorial thiab siv nws rau daws sib npaug, kev pab raws qib thiab li ntawd. Yog li ntawd, combinatorial plays ib qho tseem ceeb luag hauj lwm nyob rau hauv ntxiv kev kawm ntawv.

Combinatorial cov teeb meem: dab tsi yog lawv rau?

Yog hais tias koj paub dab tsi ib combinatorial teeb meem, tsis muaj teeb meem nrog rau lawv cov kev txiav txim siab koj yuav muaj kev. Txoj kev ntawm kev daws lawv yuav pab tau, yog tias tsim nyog, kev teem sij hawm, ua hauj lwm lub sij hawm, raws li tau zoo raws li txoj zauv, rau cov uas ua tau zoo yog tsis haum hluav taws xob.

Nyob rau hauv tsev kawm ntawv nrog rau kev tshawb nrhiav txog kev kawm txog zauv thiab computer science combinatorial teeb meem yog kawm ntxiv, rau qhov no yog ib tug tshwj xeeb kev kawm, manuals, thiab paub tab. Raws li ib tug txoj cai, ob peb cov teeb meem ntawm no hom yuav ua tau ib feem ntawm cov unified lub xeev xeem nyob rau hauv kev kawm txog zauv, lawv mas feem ntau yog "thaum" nyob rau hauv Part C.

Yuav ua li cas los daws kom tau ib tug combinatorial teeb meem sai sai?

Nws yog ib qho tseem ceeb yuav tsum tau mus ntsib tus combinatorial teeb meem sai sai, vim nws yuav tsum veiled hais, nws yog tshwj xeeb tshaj yog ib qho tseem ceeb thaum noj cov tub ntxhais, qhov chaw uas txhua feeb suav. Sau nyias cov ntaub ntawv uas koj pom nyob rau hauv cov ntawv nyeem ntawm qhov teeb meem, nyob rau ntawm daim ntawv, thiab ces sim rau kev tsom xam los ntawm tus taw tes ntawm view ntawm cov plaub nto moo txoj kev.

Yog hais tias koj muaj peev xwm muab cov ntaub ntawv nyob rau hauv ib tug spreadsheet los yog lwm yam chaw, sim mus daws tau. Yog hais tias peb cais nws, koj tsis tau, nyob rau hauv cov ntaub ntawv no nws yog ib qhov zoo tshaj plaws tawm mus nws rau ib tug luv luv lub sij hawm thiab txav mus rau mus rau lwm cov kev pab raws qib, thiaj li tsis mus nkim precious lub sij hawm. Qhov no qhov teeb meem yuav zam tau nyob rau hauv ua ntej poreshat qhov nqi ntawm no hom ntawm qhov teeb meem.

Kuv yuav nrhiav tau ib co kev piv txwv?

Qhov tshaj plaws xwb uas yuav pab tau koj kawm tau li cas los daws kom tau combinatorial teeb meem - piv txwv. Lawv muaj peev xwm yuav nrhiav tau nyob rau hauv tshwj xeeb zauv collections, uas yog muag nyob rau hauv lub khw ntawm kev kawm ntaub ntawv. Txawm li cas los, muaj peev xwm yuav nrhiav tau cov ntaub ntawv tsuas yog rau cov tub ntxhais kawm ntawv, cov tub ntxhais kawm yuav tau nrhiav ntxiv kev pab raws qib yuav tau yees ua txoj hauj lwm ntawm tus so ntawm cov xib fwb.

University professors ntseeg tau hais tias cov tub ntxhais kawm yuav tsum qhia thiab pheej muab lawv lwm yam kev kawm ntaub ntawv. Ib tug ntawm qhov zoo tshaj plaws collections suav hais tias "txoj kev Discrete Analysis nyob rau hauv kev daws combinatorial teeb meem", sau nyob rau hauv 1977 thiab manufactured los ntawm pheej ua publishing tsev ntawm lub teb chaws. Qhov ntawd yog qhov chaw uas koj yuav nrhiav tau cov kev pab raws qib uas tseem ceeb thaum lub sij hawm thiab nyob twj ywm siv tau niaj hnub no.

Yuav ua li cas yog tias koj xav mus ua ib tug combinatorial teeb meem?

Feem ntau cov feem ntau lub combinatorial ua hauj lwm, koj yuav tsum muaj cov xib fwb uas yuav tsum tau qhia cov menyuam kawm ntawv xav tias unconventionally. Ntawm no txhua yam yuav nyob ntawm seb lub tswv yim peev xwm ntawm tus originator. Nws yog pom zoo them sai sai mus rau lub uas twb muaj lawm collections thiab sim ua kom tau hauj lwm li hais tias nws combines ob peb txoj kev los daws kom tau nws, thiab yog txawv los ntawm phau ntawv cov ntaub ntawv.

University xib fwb nyob rau hauv no hais txog ntau yam freer tsev kawm ntawv, lawv feem ntau muab kuv cov menyuam kawm ntawv tuaj mus nrog cov neeg ua hauj lwm los ntawm lub combinatorial teeb meem ncauj lus kom ntxaws kev daws teeb meem thiab kev piav qhia ntawm txoj kev. Yog hais tias koj tsis nyob ib los yog cov lwm yam, koj yuav tau nug kev pab los ntawm cov neeg uas yeej paub lub cheeb tsam, raws li zoo raws li mus ntiav ib tug private pab qhia. Ib tug kawm teev yog txaus kom tsim tau ob peb zoo sib xws kev pab raws qib.

Combinatorics - qhov kev kawm ntawm lub neej tom ntej?

Muaj ntau cov kws txawj nyob rau hauv lub tshav pob ntawm kev ua lej thiab physics ntseeg hais tias nws yog combinatorial teeb meem yuav ua rau txoj kev loj hlob ntawm kev sciences. Suffice nws tsis yog-tus qauv mus kom ze rau kev daws ntawm lwm yam teeb meem, thiab ces peb yuav tau teb cov lus nug uas muaj twb tau ob peb centuries muaj dab kws tshawb fawb. Ib txhia ntawm lawv tiag tuav hais tias combinatorics yog ib lub cuab tam rau tag nrho cov niaj hnub science, tshwj xeeb tshaj yog qhov chaw tshawb kawm. Nws yog yooj yim npaum li mus laij tau qhov trajectory ntawm cov sib ntaus ntawm ships siv combinatorial teeb meem, raws li lawv yuav txiav txim seb lub caij nyoog qhov chaw ntawm tej yam xilethi-aus lub cev.

Cov kev siv uas tsis yog-tus qauv mus kom ze tau ntev pib nyob rau hauv teb chaws Es Xias, nyob qhov twg tub ntxhais kawm ntawv theem pib paub tab ntawm kev ua lej khu, kev rho tawm, ntxiv thiab faib los txiav txim siv combinatorial txoj kev. Rau cov surprise ntawm ntau European zaum, tus txheej txheem tiag tiag xwb. European lub tsev kawm ntawv nyob deb ces tsuas pib kawm los ntawm qhov kev paub ntawm lawv cov lug txhawb cov miv. Thaum nws combinatorics ua ib tug ntawm cov loj ceg ntawm kev kawm txog zauv, kev pov plob yooj yim. Tam sim no science yog kawm los ntawm ua zaum ntawm lub ntiaj teb no uas xav popularize nws.