Ungabala yonke into. Izinto ze-combinatorics

Isixhobo sehlabathi sithatha ubungqina benani elikhulu lezinto ezihlukeneyo kunye nezinto. Ngexesha elifanayo isayensi ibonisa ukuba isiseko sobuninzi sisethi yenani elithile lezinto. Ukudibanisa ngeendlela ezahlukeneyo, ezi zitena zibe sisiseko sokwakhiwa kwezakhiwo zehlabathi ezisijikelezayo. Ukufundelwa kwenani lazo zonke iimeko ezikhoyo zendibaniso ehlukeneyo ziqwalaselwa ngamathematika, ngokukodwa, icandelo layo, elibizwa ngokuba yi-combinatorics.

Ngoko, ixabiso elichanekileyo, isetyenzisi (ukuvumela, ukudibanisa, izibalo kunye nokubekwa kwezinto), kwakunye nobudlelwane nabo (njengendlela yokukhetha, ukulandelwa okuyingxenye) kuthathwa njengezinto zokufunda. Izinto ze-combinatorics zinobudlelwane obusondeleyo nejometri kunye ne-algebra, ngokuqhelekileyo zaba zizathu zokubala kwi-theory. Uluhlu olubanzi kakhulu lweendawo ezahlukeneyo zolwazi alukwazi ukucingelwa ngaphandle kokusebenzisa le ntsimi yesayensi. Eyona nto ifunwa yili candelo leemathematika liye kwi-physics, i-genetics kunye ne-informatics.

Kwaye ukuqala kwekota "i-combinatorics" ithathe ukususela ngo-1666. Ngomsebenzi wakhe "Iingxoxo malunga nobugcisa bokudibanisa," u-Leibniz wemathematika wabeka isiseko sokuphuhliswa kweli candelo lemathematika.

Ngokuqhelekileyo, usebenzisa igama elithi "i-combinatorics", qwalasela inxalenye enkulu yemathematika edibeneyo, equka, umzekelo, igraphic theory.

Izixhobo ze-combinatorics zivame ukuhanjiswa njengemizekelo yokuqwalasela idibanisa. Ukubekwa, imvume, ukudibanisa, ukubunjwa kunye nokwahlukana kwenani yimiba ephambili apho imigaqo yale candelo yeemathematika ifakiwe.

Ukubekwa isethi esimiselweyo yenani elithile lamacandelo esethi ethile, kunye nenani elicacileyo lezinto. I-permutation isetyenziswe ngokucwangcisiweyo ngokuqinileyo kwenani elinqunyiwe lezinto. Inhlanganisela yokuhlanganiswa - isethi yenani lezinto ezifakwe kwi data. Iikiti zineenkcenkceshana kuphela ngokulandelelaniswa kwezinto, kodwa zifana nokubunjwa, lo ngumlinganiselo phakathi kokuhlanganiswa kunye nokubekwa. Inani lenhlanganisela luxhomekeke kubukhulu besethi kunye nenani lezinto ezenza isethi, apho amanani asetshenziselwa ukuqokelela imodeli yokudibanisa.

Ukuqwalasela ingcamango yokubunjwa kwenani, thabatha naluphi na ummeli njengesixa-mali, esalawulwe kwii-integers ezintle. Kodwa ukwahlula kwenani naluphi na ukubonakaliswa kwalo njengesixa esingahambelananga seenombolo ezipheleleyo.

Izinto ze-combinatorics zifumene izicelo ezininzi kwiinkalo ezihlukeneyo zolwazi. Ngelo xesha, le nxalenye yeemathematika ngokwayo yaphuhliswa ngokukhawuleza okwenza yonke imithwalo yempahla eqokelelwa kulo mkhakha iza kubelwa kwicandelo.

Ukuqwalasela icandelo loqeqesho olubizwa ngokuthi "i-combumeratoric enumerative" (ukubala), qwa lasela iibalo okanye ubale inani lazo zonke iinkqubo ezikhoyo (umzekelo, iimvume) ezenziwe kwizinto zeefomite ezigqibeleleyo. Kunokwenzeka ukubeka imithintelo ethile. Oku kubandakanya ukungaqondi okanye ukuqonda izinto, isisombululo sokuphindaphinda kwizinto ezifanayo, njl.

Ukubala inani loqwalaselo, sebenzisa imithetho yeklasi yokuphindaphinda nokudibanisa. Izinto zezinto zokudibanisa zivela kule candelo loqeqesho zizisetyenziselwa ukujongana neentlobo ezahlukeneyo zemisebenzi.

Imininzi yemibuzo kwi-theory yegrafu yongezwa kwi-combinatorics , kunye nefuthe lemfundiso ye-matroid. Phakathi kwamacandelo okuqeqesha kukho ukudibanisa okugqithisileyo, i-Ramsey theory, i-prognilistic, inpological, ne-infinitary combinatorics.