kramachaya-sanchaya

kramachaya-sanchaya (Combinatorics) ganit ki shaakha hai jismein ginne yogya vivrt (discrete) sanrachanaaon (structures) ka adhyayan kiya jaata hai.

shuddh ganit, beejaganit, praayikta siddhaant, topoloji tatha jyaamiti aadi ganit ke vibhinn kshetron mein kramachaya-sanchaya se sanbandhit samasyaaye paida hoteen hain. iske alaava kramachaya-sanchaya ka upayog ishtatameekaran (aaptimaaijeshan), sanganak vigyaan, ergodik siddhaant (ergodic theory) tatha saankhyikeeya bhautiki mein bhi hota hai. graaf siddhaant, kramachaya-sanchaya ke sabse puraane evam sarvaadhik prayukt bhaagon mein se hai. aitihaasik roop se kramachaya-sanchaya ke bahut se prashn vilgit roop mein uthate rahe the aur unke tadarth hal prastut kiye jaate rahe. kintu beesaveen shataabdi ke uttaraardh mein shaktishaali evam saamaanya saiddhaantik vidhiyaaain viksit huin aur kramachaya-sanchaya ganit ki svatantr shaakha bankar ubhara.

itihaas

kramachaya-sanchaya se sambandhit saral prashn kaafi praacheen kaal se hi uthate aur hal kiye jaate rahe hain. 6thi shataabdi isa poorv mein Bhaarat ke mahaan aayurvijnyaaani sushrut ne sushrutasanhita mein kaha hai ki 6 bhinn svaadon ke kul 63 sanchaya (kanbineshan) banaaye ja sakte hain (ek baar mein keval ek svaad lekar, ekabaar mein do svaad lekar ... is prakaar kul 26-1=25 samuchchaya ban sakte hain.) 850 isavi ke aaspaas Bhaarat ke hi ek doosare mahaan ganitjnya mahaaveer (ganitjnya) ne kramachayon evam sanchayon ki sankhya nikaalne ke liye ek saamaanyeekrut sootr bataaya. bhaarateeya ganitjnyaon ne hi dvipd gunaank nikaale jo aage chalakar paaskal trikon naam se prasiddh hue.

beesaveen shataabdi ke uttaraardh mein kramachaya-sanchaya ke adhyayan ne tvarit gati praapt ki aur is vishay ke darjanon journal astitv mein aaye tatha is vishay par kai sangoshthiyaaain huiain.

inhein bhi dekhein

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