E huli a pau e hiki ai. oihana mua o combinatorics

lima kūlana kiʻekiʻe i loko o ke ao nei presupposes ke ola ana o ka nuiʻano o nā hanana a me nā mea. I ka Ia manawa 'epekema proves i ke kumu o keia nui mea he lākou o kekahi mau helu o eiiiiiaiou. Ai pili aku i loko o ka okoa mea, i kēia mau ālai 'nō ke kumu no ka kuhikuhipuʻuone? Ieoaeunoaa iauaeoia o ko ke ao nei a puni mākou. I ka like ana o ka helu o ka hiki a pau Lolina o ka pu ana o na eiiiiiaiou likeʻole kākou i loko o makemakika, i maikai kona pauku kapaia combinatorics.

Penei, e like me ka mea o ka study discrete cia maliuia mai, he iiiaanoaa (permutations, pu ana, hoolilo a me ka hoʻokomo 'ana i na kumu mua) a me kino i ka ma luna o ia (kohoʻia hapa mea). combinatorics hehee wale i ke kokoke pilina me ka anahonua a me ka hōʻailona helu, ka mea, aneane lilo i ke kumu no ka hoʻomaulia i loko o ka kumumanaʻo o ka pahiki. Laulā huahelu o kekahi mau kihapai o ka ike mea hiki ole ke manao wale me ka hana ana o keia kahua o ka 'epekema. Ka loa kaulana lala o ka makemakika i hoomaka ma ana helu ke kālaikūlohea, aaiaoe? A kamepiula 'epekema.

A me ka hoʻomaka o kona makahiki, "combinatorial" e kaili mai 1666. I kana hana "e kamailio nei ma ka combinatorial nō" mathematician Leibniz waiho iho i ke kahua no ka hou 'ana o kēia lālā o ka makemakika.

Loa pinepine, e hoʻohana i ka makahiki "combinatorics", e lawe i ka mooolelo o ka mahele nui lehulehu o discrete makemakika, a mai nā ', no ka mea hoike, i ka kumumanaʻo o ka pakuhi.

Oihana mua o combinatorics ua pinepine hooku iho la ia me ke kumu hoʻohālike o combinatorial kŰia ke kau. Accommodation, rearrangement, me ka hui pu, haku mele 'ana a me ka paku loa i ka papa kuhikuhiE eiiiiiaiou, a i loaʻa i loko o keʻano o nā loina o kēia lālā o ka makemakika.

I hoʻokomo '- i kauoha' ia paha o kekahi mau helu o eiiiiiaiou no a hiki i ke kau, me ka luawai-hoakaka helu o ka oihana mua. Permutation kapa pololei kauoha 'ia paha o ka paa helu o ka oihana mua. Combinatorics hoʻohui pū 'ia - he i o ia ka helu o nā' ikamu i komo i loko o nā ikepili. E hoʻopaʻa i ka mea oko ao wale nō i loko o ka mea ana i na kumu mua, akā, ka mea mau i ka ua 'ole, keia mea i ka likeʻole o ka hui pu ana, a me ka hoʻokomo'. Ka helu o nā ana hilinaʻi nui ma luna o ka nui o ka i, a me ka helu o nā hehee wale ana i ka ahaaina, mai a i laweia no ka makaukau o ka la combinatorial kükohu.

E noonoo pono i ka manaʻo o ka haku mele 'ana o ka, lawe ia a pau i ka hoohalike o ke dala i kauoha mai i ka maikaʻi integers. Akā, i ka paku o ka - mea i kekahi manaʻo ana o kona kāna hana huina o maikaʻi integers.

Oihana mua o combinatorics i hoʻomano hoʻohana i loko o kekahi mau kihapai o ka ike. I ka Ia manawa ia i keia hapa o ka makemakika hala ia i ka hana keaka 'ana i ua' ā ka ka hoʻonui ukana 'ike i loko o kēia kahua e līkaia no i pohā.

E noonoo pono i ka hahau pauku noa i ka ' "Combinatorial helu" (quantifiable), e lawe i ka mooolelo o ka hoololiia ana a helu i ka helu o ka hiki kŰia ke kau (no ka laʻana, permutations), a i hana, mai na kumu mai o finite e puhi ia. He hiki i ke kau ana o kekahi mau palena. Mau nā invisibility a maopopo hehee wale, 'oe i ka olelo hooholo o ka ia hehee wale, a pela aku.

No ka ho omaulia i ka helu ana o kŰia ke kau, ka hoʻohana 'ana i ka panina rula o ka hou a me ka multiplication. Oihana mua o combinatorics i loko o kēia māhele o ka hahau hoʻohana e hoʻoponopono i ka laulā huahelu o kekahi mau hana.

Ke mall combinatorics hou i ka helu o ke kumuhana o ka pakuhi kumumanaʻo, hōʻike i ka aoao o ka pähola 'ana o matroids. Mawaena o na pauku o ka hahau ua hoi kahiāuli loa combinatorics, Ramsey kumumanaʻo, pahiki, topology, combinatorics infinitary.