Lissafi duk zai yiwu. abubuwa na combinatorics

na'urar a duniya presupposes da wanzuwar wata babbar dama events da kuma abubuwa. A lokaci guda kimiyya ya tabbatar da cewa tushen wannan yalwa ne mai sa na wani yawan aka gyara. Danganta a wani daban-daban domin, wadannan tubalan ne dalilin da gine-gine da constructions na duniya kewaye da mu. A binciken da na yawan duk yiwu bambance-bambancen karatu na a hade da daban-daban aka gyara da hannu a ilmin lissafi, musamman ta sashe kira combinatorics.

Saboda haka, kamar yadda abubuwa na nazari mai hankali dabi'u yarda, a jam'i (permutations, haduwa, canja wuri da kuma jeri na abubuwa) da kuma halaye a kan su (ba dole m domin). combinatorics abubuwa da kusa dangane da lissafi da kuma aljabara, sun yi kusa su zama tushen ga lissafin da ka'idar yiwuwa. Wide kewayon daban-daban na ilimi ne ba zai yiwu ba su yi tunanin ba tare da yin amfani da wannan filin na kimiyya. A mafi m reshe na lissafi da ya fara a ilimin kididdiga kimiyyar lissafi, halittar jini da kwamfuta kimiyya.

Kuma farkon ya ambatacce, "combinatorial" daukan daga 1666. A cikin aikinsa "Maganganu a kan combinatorial art" lissafi Leibniz aza harsashin ginin don kara raya wannan reshe na lissafi.

Sau da yawa sosai, don amfani da Kalmar "combinatorics", shan la'akari da wani yawa fadi sashe na mai hankali lissafi, wanda ya hada da, misali, ka'idar jadawalai.

Abubuwa na combinatorics ne sau da yawa gabatar a matsayin wani abin koyi na combinatorial jeri. Masauki, rearrangement, hade, abun da ke ciki da kuma bangare lambobi ne babban aka gyara, wanda ake samu a cikin embodiment ka'idojin wannan reshe na lissafi.

Jeri - wani umurni da ya kafa wani yawan aka gyara na zuwa wani sa, tare da da-tsare yawan abubuwa. Permutation kira tsananin umurni da sa wani tsayayyen yawan abubuwa. Combinatorics hade - a sa na dauka da yawan abubuwa kunshe a cikin bayanai. Sets ne bambance-bambance ne kawai a cikin tsari na abubuwa, amma su ne guda tsarin, wannan shi ne bambanci tsakanin hade da jeri. Yawan haduwa dogara a kan girman da ya kafa da kuma yawan abubuwa yin up sa, daga abin da ake dauka domin shiri na ce combinatorial model.

Idan akai la'akari da manufar abun da ke ciki na, kai da shi duk matsayin misali na adadin da umarnin daga cikin tabbatacce integers. Amma bangare na - shi ne wani ra'ayin yadda ya tarwatsettsun Naira Miliyan Xari da kyau integers.

Abubuwa na combinatorics an yadu amfani a fannoni daban daban na ilimi. A daidai wannan lokaci da ta aikata wannan ɓangare na lissafi shige da irin wannan ban mamaki ci gaba da cewa ya kunna da tara kaya bayanai a cikin wannan filin ware partitions.

Idan akai la'akari da horo sashe mai suna "Combinatorial enumeration" (tsammani), shan la'akari da canja wurin ko kirgawa yawan yiwu jeri (misali, permutations), wanda aka kafa daga abubuwa na guntun sets. Yana yiwuwa da Kaddamar da wasu hane-hane. Wadannan sun hada da invisibility ko bayyana abubuwa, maimaita ƙuduri na wannan abubuwa, da sauransu.

Don lissafta yawan jeri, ta amfani da na gargajiya dokoki na Bugu da kari kuma multiplication. Abubuwa na combinatorics a cikin wannan sashe na horo amfani da shi don warware wata fadi da kewayon daban-daban ayyuka.

A tsarin combinatorics kara wasu batutuwa na jadawali ka'idar, ya nuna tasirin da ka'idar matroids. Daga cikin sassan na horo ne ma alama matsananci combinatorics, Ramsey ka'idar, Yiwuwar, topology, combinatorics infinitary.