antichen

ganitamadhye, kram siddhantachya kshetrat, antichen haah anshatah krambaddha sanch assa upasanch aahe qee upasanchatil konatehi done bhinn ghatak atulaneey aahet.
anshatah krambaddha sanchatil sarvat mothya antichencha aakar tyachi rundi mhanoon olakhala jaato. dilworthchya prameyanusar, heey sanchache vibhajan karata yeil asha sakhalichi kiman sankhya (purnapane krambaddha upasanch) dekhil aahe. duheri, anshatah krambaddha sanch (tyachya sarvat lamb sakhalichi lambi) chee unchi mirskeechya prameyanusar antichenchya kiman sankhyeitaki asate jyamadhye sanch vibhajit keela jaau shakato.
maryadit anshatah krambaddha sanchatil serve antichenchya kutumbala join aanee meat operations dile jaau shakatat, jyamule teey vitaran jaali banatat. maryadit sanchatil serve upasanchanchya anshatah krambaddha pranalisathi, sanch samaveshakatenusar krambaddha, antichenna shukranu kutumbe mhanatat
aanee tyanchi jaali hii ghatakanchi sankhya qamee asalelya mukt vitaran jaali aahe. adhik samanyatah, maryadit anshatah krambaddha sanchatil pratishrunkhalechi sankhya mojane #p-purn aahe.
vyakhya.
sootra _ 1 haah anshatah krambaddha sanch asoo dya. jarr sootra 4 madhye done ghatak tulanatmak nastil tarr, tyanna atulaneey mhatale jaate; mhanje, sootra 5 aanee sootra 6 heey donhi sootra 7 madhye naslyas atulaneey aahet.
sootra _ 1 madheel sakhali heey eka upasanch sootra _ 9 aahe jyamadhye ghatakanchi pratyek jodee tulanatmak aahe; mhanje sootra _ 10 purnapane krambaddha aahe. sootra _ 1 madheel antichen heey sootra _ 1 chey upasanch sootra _ 12 aahe jyamadhye vegvegalya ghatakanchi pratyek jodee atulaneey aahe; mhanje, sootra _ 14 madheel konatyahi done bhinn ghatakanmadhye konatahi kram sambandh nahee. 
unchi aanee rundi.
maximal antichen haah eka antichen aahe joou itar konatyahi antichencha yogya upasanch nahee. kamal antichen hii eka antichen aahe, jyachi cardinality itar pratyek antichenaitakich mothee aahe. anshatah krambaddha kelelya sanchatil 'daad' hii kamal antichenchi mukhyata aahe. konatihi antichen konatyahi sakhalila jastit jaast eka ghatkamadhye chhedu shakate, mhanoon jarr aapan kramachya ghatakanche sootra _ 15 sakhalyanmadhye vibhajan karoo shakalo tarr kramachi rundi jastit jaast sootra _ 15 asane aavashyak aahe (jarr antichenmadhye sootra _ 15 peksha jaast ghatak asateel, tarr kabootar chhidra tattvanusar, tyach sakhalishi sambandhit tyache 2 ghatak asateel, eka virodhabhas). dilworthche pramey asey sangate qee hii seema nehmich gathali jaau shakateh nehmich eka antichen astitvat asate aanee ghatakanche sakhalyanmadhye vibhajan asey asate qee sakhalyanchi sankhya antichenmadhil ghatakanchya sankhyeitaki asate, jee rundichya barobarichi dekhil asane aavashyak aahe. tyachpramane, ekhadi vyakti aanshik kramachi sakhalichi kamal mukhyata mhanoon vyakhya karoo shakate. mirskyche pramey asey sangate qee maryadit unchichya konatyahi aanshik kramane, unchi hii antichenchya sarvat lahan sankhyeaevadhi asate jyamadhye kramache vibhajan kele jaau shakate.
shukranunchi kutumbe.
sootra _ 18-ghatak sanchachya upasanchanchya samavesh kramanusar antichenla shukranu kutumb mhanoon olakhale jaate. vegvegalya shukranunchya kutumbanchi sankhya hii dedeckind sankhyandvare mojali jaate, jyapaiki pahilya kahee sankhya aahet -
rikamya sanchamadhyehi tyachya shakti sanchamadhye done pratishrunkhale asatatah eka sanch ekach (rikama sanch swatach) aanee eka sanch nasalela.
karyat sameel vha aanee tyanchi purtata qaraa.
konatehi antichen sootra _ 12 khalchya sanchala anuroop aahe
sootra _ 20
maryadit aanshik kramane (kinwa adhik samanyatah chadhatya sakhalichi sthitee purn karnari aanshik kramane) serve khalchya sanchanna heey swaroop asate. konatyahi done khalchya sanchanche sanyojan haah aanakhi eka khalcha sanch aahe aanee sangh karya asha prakare jode operationshee sambandhit aahe.
antichenvarh
sootra _ 21
tyachpramane, aapan khalchya sanchanchya chhedanbindubaddal, antichenvar meat operation paribhashit karoo shakatoh
sootra _ 22
23 yaa sanch sootrachya maryadit upasanchanchya serve maryadit pratishrunkhalanvar jodane aanee purn karane heey karya vitaran jaali paribhashit karate, vitaran jaalisathi 24 bercoffchya pratinidhitva prameyadvare tayar kelele mukt vitaran jaali asey sangate qee pratyek maryadit vitaran jaali maryadit aanshik kramachya pratishrunkhalanvar jodane aanee karye purn karane, kinwa aanshik kramachya khalchya sanchanvaril sangh aanee chhedanbindu karye yasarkhya samatulya paddhatine darshavili jaau shakate.
sanganakeey jatilata.
bahupadichya velet kamal antichen (aanee tyacha aakar, dilelya anshatah krambaddha kelelya sanchanchi rundi) aadhalu shakate.
dilelya anshatah krambaddha kelelya sanchatil antichenchi sankhya mojane #p-purn aahe.

