
latin chadarapu

combinatorics mariyu prayogaatmaka roopakalpanalo, latin square anedi "n" × "n" shrenilo "n" ververu chihnalatho nindi untundi, prati varusalo sarigga okasari mariyu prati niluvu varusalo sarigga okasari sambhavistundi. 3x3 latin chaturasraaniki udaaharana
latin aksharaalanu chihnaluga upayoginchina leonhard euler (1707-1783) ganita patraala nundi "latin square" anae paeru prerana pondindi, conny yea chihnala samitini ayina upayoginchavachhuh paie udaaharanalo, aksharakrama kramam a, b, c nii puurnaanka kramam 1,2,3 dwara bharti cheyavachu. euler latin chaturasraala yokka saadhaarana siddhaantaanni praarambhinchaadu.
charitra.
corian ganita shaastravetta choyi seok-jiong 1700loe leonhard yoolarku 67 samvatsaraala mundu oka maaya chaturasraanni nirminchadaaniki, tommidi kramamlo unna latin chaturasraala udaaharananu prachurinchina modati vyakti.
taggina roopam.
latin chaturasram daani modati varusa mariyu daani modati niluvu varusa rendoo vaati sahaja kramamlo unte "tagginchabadindi" (kooda, "saadhaaraneekarinchabadindi" ledhaa "praamaanika roopamlo") anie chebutaaru. udaaharanaku, paina unna latin chaturasram tagginchabadaledu endukante daani modati niluvu varusa a, b, c kakunda a, c, b.
varusalanu mariyu niluvu varusalanu kramabaddhikarinchadam (antey, punahkramam cheyadam) dwara edainaa latin chaturasraanni tagginchavachhu. ikkada paina perkonna maatrika yokka rendava mariyu moodava varusalanu marchadam valana eee krindi chaturasram labhistundihi
eee latin chaturasram tagginchabadindi; daani modati varusa mariyu daani modati niluvu varusa rendoo aksharakramamlo a, b, c gaa kramabaddheekarinchabaddayi.
aastulu.
orthogonal shreni praatinidhyam.
n" × "n" latin chaturasram yokka prati namodu triple ("r", "c", "s") gaa vraayabadithe, ikkada "r" anedi varusa, "c" anedi niluvu varusa, mariyu "s" anedi chihnam, manam "n" 2 triples samitini pondutaamu, dheenini chaturasram yokka orthogonal shreni praatinidhyam anie pilustaaru. udaaharanaku, latin chaturasram yokka orthogonal shreni praatinidhyam
idhi
udaaharanaku triple (2,3,1) antey varusa 2 mariyu niluvu varusa 3 loe chihnam 1 undhi. orthogonal shrenulu saadhaaranamgaa shreni roopamlo vraayabadataayi, ikkada triples varusalu, avih
latin chaturasram yokka nirvachananni orthogonal shrenula paramgaa vraayavachuhu 
dheeni ardham "n" 2 kramabaddheekarinchina jatala ("r", "c") annee jatala ("i", "j") 1 ≤ "i", "j" ≤ "n", okkokasari. kramabaddheekarinchina jatalaku ("r", "s") mariyu kramabaddheekarinchina jatalaku ("c", "s") kooda idhe vartistundi.
orthogonal shreni praatinidhyam varusalu, niluvu varusalu mariyu chihnalu chaalaa saaruupya paatralanu poeshistaayani choopistundi, idhi krinda spashtamgaa untundi.
latin chaturasraala samanatva taragatulu.
latin chaturasrampai aneka karyakalapalu maroka latin chaturasraanni utpatti chestaayi (udaaharanaku, daanini talakrindulugaa tippadam).
manam varusalanu kramabaddheekariste, niluvu varusalanu kramabaddheekariste ledhaa latin chaturasram yokka chihnala paerlanu kramabaddheekariste, modatidaaniki "isotopic" anie cheppabade kotta latin chaturasraanni pondutaamu. isotopism anedi oka samanatva sambandham, kabatti anni latin chaturasraala samitini "isotopy taragatulu" anie piluvabade upasamitulugaa vibhajistaaru, antey oke taragatiloni rendu chaturasraalu isotopic mariyu vividha taragatulaloni rendu chaturasraalu isotopic kaavu.
latin square yokka orthogonal arre praatinidhyaanni upayoginchi maroka rakamaina operation vivarinchadam sulabham. prati triple loe moodu amsaalanu kramabaddhamgaa mariyu sthiramgaa kramabaddheekariste (antey, arre roopamlo moodu niluvu varusalanu kramabaddheekarinchandi), maroka orthogonal arre (mariyu, tadwara, maroka latin square) pondabadutundi. udaaharanaku, manam prati triple ("r", "c", "s") nuu ("c", "r", "s") thoo bharti cheyavachu, idhi squarenu badilee cheyadaaniki (daani pradhana vikarnam gurinchi pratibimbistumdi) anugunamgaa untundi, ledhaa manam prati triple ("r", "c", "s") nuu ("c", "s", "r") thoo bharti cheyavachu, idhi marinta sanklishtamaina operation. aemee cheyavaddu" thoo sahaa mottam 6 avakaasaalu unnaayi, idhi asalu chaturasram yokka samyogaalu (parastrophelu kooda) anie piluvabade 6 latin chaturasraalanu istundi.
chivaraku, manam eee rendu samanatva karyakalapalanu kalapavacchuhu rendu latin chaturasraalu "paratopic" anie cheppabadataayi, vaatilo okati isotopic mariyu marokati samyogam ayithe "pradhana taragati isotopic" anie kooda cheppabadutundi. idhi mallii "pradhana taragatulu", "jaatulu" ledhaa "paratopy taragatulu" anie piluvabade samanatva taragatulato samanatva sambandham. prati pradhana taragatilo aaru isotopy taragatulu untaayi.
latin chaturasraala sankhya.
chihnalatho kuudina latin chaturasraala sankhyaku sulabhamgaa ganinchadagina suutram ledhu. peddavigaa telisina atyanta khachitamaina eguva mariyu diguva sarihaddulu chaalaa dhooramlo unnaayi. oka praamaanika phalitam emitante
suutram _ 1
latin chaturasraala sankhyaku oka saralamaina mariyu spashtamaina suutram 1992loe prachurinchabadindi, conny padaala sankhyalo ghaataanka perugudala kaaranamgaa idhi ippatikee sulabhamgaa lekkinchabadadu. latin chaturasraala sankhyaku eee suutram
suutram _ 2
anni {0,1}-maatrikala samiti ekkada undhi, idhi maatrikalo sunna namodula sankhya, mariyu idhi maatrika yokka shaashwata sankhya.
diguva pattikalo telisina anni khachitamaina viluvalu unnaayi. eee sankhyalu chaalaa vaegamgaa perugutaayani chudavachu. pratidaaniki, mottam latin chaturasraala sankhya taggina latin chaturasraala sankhyaku rettimpu.
pratidaaniki, prati isotopy taragatilo latin chaturasraala varaku untaayi (khachitamaina sankhya maarutuu untundi), ayithe prati pradhana taragatilo 1,2,3 ledhaa 6 isotopy taragatulu untaayi.
nirmanatmakamga vibhinnamaina latin chaturasraala sankhya (i.ii. = 1 nundi 7 varaku varusaga 1,1,1,12,192,145164,1524901344 varaku) kosam, chaturasraalanu bhramanam, pratibimbam mariyu/ledhaa chihnala kramaparivartana dwara okela cheyalemu.
udaaharanalu.
prati pradhana taragati nundi aidu arder varaku latin squareku oka udaaharana istaamu.
suutram _ 3
suutram _ 4
suutram _ 5
avi varusaga, eee krindi samuuhaala gunana pattikalanu pradarsistaayih
transversals mariyu indradhanassu matchlu.
latin chaturasramlo transversal anedi "n" kanaala empika, ikkada prati varusalo oka kanam untundi, prati niluvu varusalo oka kanam untundi mariyu prati chihnanni kaligi unna oka kanam untundi.
latin chaturasraanni puurti dwaipaakshika rekhaachitramgaa pariganinchavacchu, dheenilo varusalu oka bhaagam yokka sheershaalu, niluvu varusalu maroka bhaagam yokka sheershaalu, prati kanam oka anchu (daani varusa mariyu daani niluvu varusa madhya), mariyu chihnalu rangulu. latin chaturasraala niyamaalu idhi saraina anchu rangu anie suuchistaayi. eee nirvachanamtho, latin transversal anedi prati anchu ververu rangunu kaligi unna oka saripolika; atuvanti saripolikanu indradhanassu saripolika antaaru.
anduvalla, latin chaturasraalu/deerghachaturasraalapai aneka phalitaalu vaati sheershikalo "indradhanassu saripolika" anae padamtho kaagitaalalo untaayi, mariyu dheeniki viruddhamgaa untaayi.
konni latin chaturasraalaku transversal undadu. udaaharanaku, "n" anedi sarri ayinappudu, oka "n"-bye-"n" latin square, dheenilo sell "i" viluva, "j" anedi ("i" + "j") mode "n" anedi transversal kaadu. ikkada rendu udaaharanalu unnaih 1967loe suutram _ 11, h. zhe. n" besigaa unnappudu, prati "n"-bye-"n" latin chaturasram oka transversal kaligi untundani raisar oohinchaaru.
1975loe, ess. keey. n" anedi sarri ayinappudu, prati "n"-bye-"n" latin chaturasram parimaanam "n"-1 yokka pakshika vilomam kaligi untundani steyn mariyu brouldi oohinchaaru.
steyn yokka marinta saadhaarana ooha emitante, latin chaturasraalalo matrame kakunda, prati chihnam sarigga "n" saarlu kanipinchinanta varaku, "n"-1 parimaanam yokka vilomam "n"-1 "n" chihnala yokka edainaa "n"-bye-"n" shrenilo kooda untundi.
eee anchanaala yokka konni balaheenamaina samskaranalu niroopinchabaddaayih
algorithamlu.
chinna chaturasraalaku prastaaranalanu utpatti cheyadam mariyu latin chadarapu lakshanam neraverutundaa anie pareekshinchadam saadhyamavutundi. pedda chaturasraala kosam, jacobson mariyu mathuse algorithm "n" × "n" latin chaturasraala sthalamlo ekareeti pampinhee nundi namuunaanu anumatistundi.
applications.
kodlanu sarididdadamlo lopam.
okadaanikokati artogonalga unde latin chaturasraala setlu, powerlinela dwara broadband internetnu prasaram cheyadaaniki prayatninchinappudu, saadhaarana tellani sabdam kante ekkuva rakaala sabdaala dwara communicationku bhangam kaliginche paristhitulalo doshaanni sarichese sanketaalugaa oka anuvartanaanni kanugonnayi.
modata, sandesam aneka pounahpunyaalu ledhaa chaanellanu upayoginchadam dwara pampabadutundi, idhi oka saadhaarana paddhati, idhi edainaa oka nirdishta pounahpunyamlo signalnu sabdam yokka takkuva haani kaliginchela chestundi. pampavalasina sandesamloni oka lekha varusa samaya vyavadhilo ververu pounahpunyaala vadda sankethaala shrenini pampadam dwara encode cheyabadutundi. diguva udaaharanalo, a nundi l varaku aksharalu naalugu ververu pounahpunyaala vadda, naalugu samaya slaatlalo sankethaalanu pampadam dwara encode cheyabadataayi. udaaharanaku, c aksharam modata 3, taruvaata 4,1 mariyu 2 frequency vadda pampadam dwara encode cheyabadutundi.
suutram _ 12
pannendu aksharaala encoding okadaanikokati orthogonal ayina moodu latin chaturasraala nundi erpadataayi. ippudu mottam prasaara samayamlo chaanallu 1 mariyu 2 loe adanapu sabdam undani oohinchukondi. appudu a aksharam ilaa teeyabadutundihi
suutram _ 13
maroe maatalo cheppalante, modati slaatlo manam frequency 1 mariyu frequency 2 rendinti nundi sankethaalanu andukuntamu; moodava slaatlo frequency 1,2 mariyu 3 nundi sankethaalu unnaayi. sabdam kaaranamgaa, modati rendu slaatlu 1,1 ledhaa 1,2 ledhaa 2,1 ledhaa 2,2 anie manam ikapai cheppalemu. conny 1,2 kesu matrame paie pattikalooni aksharaniki saripoye kramaanni istundi, aksharam a. 
adevidhamgaa, moodava slaatlooni anni frequencilapy sthiramaina paeludunu manam oohinchavachhuh
suutram _ 14
mallii, encodingla pattika nundi adhi prasaram cheyabadutunna aksharam ayi undaali anie manam oohinchagalugutaamu. eee code gurtinchagala lopaala sankhya samaya slaatla sankhya kante okati takkuvagaa untundi. pounahpunyaala sankhya prime ledhaa prime yokka power ayithe, orthogonal latin squarelu veelainanta samarthavantamgaa doshaanni gurtinche sankethaalanu utpatti chestayani kooda niroopinchabadindi.
ganita puzzles.
paakshikamgaa nindina chaturasraanni latin chaturasraanni roopondinchadaaniki puurti cheyavacha anie nirnayinche samasya np-puurti.
prasiddha sudoku puzzles latin chaturasraala yokka pratyeka kesu; sudoku puzzle kii edainaa parishkaram latin chaturasram. tommidi pratyeka 3x3 prakkane unna upavargaalu kooda 1-9 ankelanu kaligi undaali (praamaanika samskaranalo) anae adanapu parimitini sudoku vidhistundi. sudoku yokka ganitaanni kooda chudandi.
iteevali kenken mariyu strinco puzzles kooda latin chaturasraalaku udaaharanalu.
boardu games.
latin chaturasraalu aneka boardu atalaku aadhaaramgaa upayoginchabaddaayi, mukhyamgaa prajaadarana pondina nairoopya vyuuhaatmaka aata camisado.
vyavasaya shaastra parisoedhana.
prayogaatmaka lopaalanu tagginchadaaniki vyavasaya parisoedhana prayogaala roopakalpanalo latin chaturasraalu upayoginchabadataayi.
vamsapaaramparya.
latin chaturasram kooda kenada ganaanka samajam yokka chetullo undhi, daani blazonelo pratyaekamgaa prastaavinchabadindi. alaage, idhi antarjaateeya biometric society logolo kanipistundi.

