
yuva tablo

ganithashaasthrathil, oru yuva tablo (bahuvachanam tablo) praathinidhya sidhaanthathilum shubert calculusilum upayogapradamaaya oru samyojitha vasthuvaan. samamiti, pothuvaaya rekheeya grouppukalude group praathinidyangal vivarikkunnathinum avayude gunangal padikkunnathinum ithu oru soukaryapradamaaya maarggam nalkunnu. 1900-ll kembridge sarvakalaashaalayile ganithashaasthranjanaaya alfred yamgaanu yuva tablo avatharippichathu. 1903-ll jorg frobinius avaa samamiti grooppinekkurichulla padanatthinu prayogichu. avarude sidhaantham persey mcmohan, dablyu. vii. dii. hodge, jii. dii bii. robinson, jian-carlo rotta, alan lascox, marsell-pooll shutsenberger, richard pii. staanli.
nirvachanangal.
"kurippu eee lekhanam yuva rekhaachithrangalum tablox pradarshippikkunnathin engleesh kanvenshan upayogikkunnu".
rekhaachitrangal.
oru yuva rekhaachithram (ferrer diagram ennum vilikkunnu, prathyekichu dottukal upayogichu prathinidheekarikkumbol) idathu nyaayeekarikkapetta varikalil krameekarichirikkunna boxukaludeyo cellukaludeyo parimithamaaya shekharamaanu, varikalude neelam vardhikkaatha kramatthil. oro variyileyum boxukalude ennam pattikappeduthunnathu oru noonn-negatteevu poornnasamkhyayude oru partition nalkunnu, ithu rekhaachithrathile boxukalude aake ennamaanu. yuva rekhaachithram aakruthiyilullathaanennum athu aaa vibhajanathinte athe vivarangal vahikkunnuvennum parayappedunnu. oru yuva rekhaachithram mattonnil ulppeduthunnathu ellah paarteeshanukaludeyum koottatthil oru bhagika kramatthe nirvachikkunnu, ithu yadhaarthathil youngs laattis ennariyappedunna oru laattis gadanayaanu. oro nirayileyum oru yuva rekhaachithrathinte boxukalude ennam pattikappeduthunnathu mattoru partition nalkunnu, konjugettu allengil transpose partition; oraalkk aaa aakruthiyude oru yuva rekhaachithram athinte pradhana diagonaliloode yadhaartha rekhaachithram prathifalippichukondu labikkum.
yuva rekhaachithrangalude labeling boxukalil jody poornnasamkhyakal upayogichu, aadya soochika rekhaachithrathinte varii thiranjedukkunnu, randaamathe soochika variyile petti thiranjedukkunnu enna kaaryatthil eathaandu saarvathrikamaaya daaranayundu. ennirunnaalum, eee rekhaachitrangal pradarshippikkunnathin rund vyathyastha kanvenshanukal nilavilundu, thalphalamaayi tablo aadyathethu oro variyum mumbathethinu thaazheyum randaamathe staakk oro variyum mumbathethinu mukalilum sthaapikkunnu. muun kanvenshan pradhaanamaayum aamglophonukal upayogikkunnathinaal randaamathethu palappozhum francophoneukal eshtappedunnathinaal, eee kanvenshanukale yathaakramam "engleesh notteshan", "franch notteshan" enningane paraamarshikkunnath pathivaanu; udaaharanathinu, cemetric functionukalekkurichulla thante pusthakatthil, franch kanvenshan eshtappedunna vaayanakkaare "eee pusthakam kannaadiyil thalakeezhaayi vaayikkaan" mcdonald upadeshikkunnu (mcdonald 1979, peju. 2). eee naamakaranatthinte thudakkam orupakshe haasyaroopathilaayirikkaam. engleesh notteshan maatriksukalkkayi saarvathrikamaayi upayogikkunnathinu anuyojyamaanu, athesamayam franch notteshan cartician kordinettukalude kanvenshanumaayi aduthirikkunnu; ennirunnaalum, lamba coordinate aadyam sthaapikkunnathiloode franch notteshan aaa kanvenshanil ninnu vyathyasthamaan. valathuvashathulla chithram, engleesh notteshan upayogichu, 10-aamm nambarinte partition (5,4,1)-maayi bandhapetta yuva rekhaachithram kaanikkunnu. koolam dairkhyam alakkunna konjugettu partition (3,2,2,1) aanu.
kaii, call ennivayude neelam.
pala prayogangalilum, udaaharanathinu jacq functionukal nirvachikkumbol, oru boxinte "a" λ (s ") nte neelam engleesh notteshanile rekhaachithrathile" s "nte valathuvashathulla boxukalude ennamaayi nirvachikkunnath soukaryapradamaanu. athupole, legg neelam "l" λ ("s") ennathu "s" nuu thaazheyulla boxukalude ennamaanu. oru boxinte "s"-nte hook neelam ennathu "s" enna boxes ulppede engleesh notteshanil "s"-nte valathuvashatho allengil "s"-nuu thaazheyo ulla boxukalude ennamaanu; mattoru vidhathil paranjaal, hook neelam "a" λ ("s") + "l" λ ("s") + 1 aanu.
tablos.
saadhaaranayaayi poornnamaayum krameekaricha oru koottamaayirikkenda chila "aksharamalaya" ll ninnu edutha chinnangal upayogichu yuva rekhaachithrathinte boxukal nirachukondaanu oru yuva tablo labhikkunnath. yadhaarthathil aaa aksharamala soochikayilulla veriyabilukalude oru koottamaayirunnu...ennaal ippol oraal saadhaaranayaayi hraswathaykkaayi oru koottam samkhyakal upayogikkunnu. samamiti grouppinte praathinidyangalilekkula avarude yadhaartha prayogatthil, yuva tablocukalkku vyathirikthamaya entrikal undu, avaa diagraminte boxukalkku ekapaksheeyamaayi nalkiyirikkunnu. oro variyileyum oro nirayileyum entrikal vardhikkukayaanenkil oru tablo staanderd ennu vilikkunnu. entrikalile vyathyastha staanderd yuva taablokalude ennam involsion nambarukal nalkunnu
mattu prayogangalil, ore samkhya oru tabloyil onniladhikam thavana (allengil ottum allah) prathyakshappedaan anuvadikkunnathu swaabhaavikamaanu. oro variyilum entrikal durbalamaayi vardhikkukayum oro nirayilum karsanamaayi vardhippikkukayum cheythaal oru tablo semi staanderd allengil koolam strict ennu vilikkunnu. oro samkhyayum oru tabloyil ethra thavana prathyakshappedunnu ennathinte ennam rekhappeduthunnathu tabloyude bharam ennariyappedunna oru kramam nalkunnu. athinaal saadhaarana yuva taablokkukal krithyamaayi ardhamaanamulla tablos aanu (1,1..1), athaayath oro poornnasamkhyayum krithyamaayi oru thavana sambhavikkendathundu.
oru saadhaarana yuva tabloyil, formula _ 2 formula _ 1 nuu karsanamaayi thaazheyulla oru variyil prathyakshappettal poornnasankhya formula _ 1 oru irakkamaanu. avarohanangalude aakethukaye tabloyude pradhana soochika ennu vilikkunnu.
vyathiyanangal.
eee nirvachanathinu niravadhi vyathiyaanangalund udaaharanathinu, oru varii-karsanamaaya tabloyil entrikal varikaliludaneelam karsanamaayi vardhikkukayum nirakal durbalamaayi vardhippikkukayum cheiyunnu. koodaathe, playin paarteeshanukalude sidhaanthathil "kurayunna" entrikalulla taablokalum pariganichittundu, prathyekichu. domino tablo allengil riban tablo polulla saamaanyavalkkaranangalum undu, athil entrikal nalkunnathinumumbu niravadhi boxukal orumichu groupucheyyaam.
table tablos.
oru vakra aakruthi ennathu oru jodi paarteeshanukalaanu (,), athaayath yuva rekhaachithrathil ithinte yuva rekhaachithram adangiyirikkunnu; ithu soochippikkunnathu. appol rekhaachithrangalude niyanthranam ardhamaakkunnathu ellaavarkkum ennaanu. oru vakra aakruthiyude vakra rekhaachithram aandam enna chithratthil ulppedunna ennaal athallaatha chathurangalude koottatthinte yuva rekhaachithrangalude settu-saidhaanthika vyathyaasamaan. anubandha scue diagraminte chathurangal nirachukondu aakruthiyude oru scue tablo labikkum; oro variyilum entrikal durbalamaayi vardhikkukayum oro nirayilum karsanamaayi vardhippikkukayum cheythaal atharam oru tablo semi staanderd aanu, koodaathe 1 muthal scue diagraminte chathurangalude ennam vareyulla ellah samkhyakalum krithyamaayi oru thavana sambhavikkukayaanenkil athu staanderd aanu. paarteeshanukalil ninnu avayude yuva rekhaachithrangalilekkulla bhoopadam kuthivayppullathaanenkum, vakra aakruthikal muthal vakra rekhaachitrangal vareyulla bhoopadatthinte kaaryatthil ithu anganeyalla; athinaal oru vakra rekhaachithrathinte aakruthi ellaayppozhum niracha chathurangalude koottatthil ninnu maathram nirnnayikkaan kazhiyilla. thirascheenamaaya pattikakalude pala savisheshathakalum niracha chathurangale maathram aashrayichaanenkilum, avayil nirvachichirikkunna chila pravarthanangalkku vyakthamaaya arivu aavasyamaanu, athinaal thirascheenamaaya pattikakal eee vivarangal rekhappeduthendathu pradhaanamaann rund vyathyasthamaaya thirascheenamaaya pattikakal avayude aakruthiyil maathram vyathyaasappedaam, athesamayam avaa ore chathurangalude koottam ulkkollunnu, oronnum ore entrikal kondu nirachirikkunnu. shoonyamaaya partition (0) (0-nte athulyamaaya partition) ulla vakramaaya tablo upayogichu yuva taablokale thirichariyaan kazhiyum.
positteev poornnasankhya entrikalulla aakruthiyilulla eathenkilum vakra semi staanderd tablo, aarambhikkunnathiloodeyum partition sthaanangalkku kooduthal edukkunnathiloodeyum, aaa kramatthil ninnu diagram labhikkunnathil ninnu oru moolyam ≤ inn adangiyirikkunna ellah boxukalum cherkkunnathiloode, paarteeshanukalude oru shreniyilekku (allengil yuva diagramukal) kaaranamaakunnu; eee partition oduvil thulyamaakum. atharam oru shreniyile thudarchayaaya aakruthikalude eathoru jodiyum oro nirayilum paramavadhi oru petti adangiyirikkunna oru vakra aakruthiyaanu; atharam aakruthikale thirashcheena strippukal ennu vilikkunnu. paarteeshanukalude eee kramam poornnamaayum nirnnayikkunnu, vaasthavathil mcdonald (mcdonald 1979, p. 4). eee nirvachanam paarteeshanukalum vakra tablo ulppedunna daattayum ulkkollunnu.
aaplikkeshanukalude avalokanam.
compinatorics, praathinidhya sidhaantham, beejaganita jyamiti ennivayil yuva tablocukalkku niravadhi prayogangalundu. yuva tablo ennunnathinulla vividha vazhikal paryavekshanam cheyyukayum shharr functionukalude nirvachanathilekkum identittikalilekkum nayikkukayum cheythu.
shutsenbergerinte jeeyu dii tackwin, robinson-shensted-nathu correspondence ennivayulppede tabloyile niravadhi samyojitha algorithangal ariyappedunnu. lascox shutsenberger ellah semi staanderd yuva tablokkukaludeyum koottatthil oru associative uthppannam padichu, ithinu "plaaktik monoid" (franch "leeii monoid plaxic") enna ghadana nalki.
praathinidhya sidhaanthathil, valippamulla staanderd yuva tablox aksharangalile cemetric grouppinte irreducible praathinidhyangalile aditharakale vivarikkunnu. pothuvaaya rekheeya grouppinte parimitha-dimensional irreducible praathinidhyatthile staanderd monomial adisthaanam {1,2, aksharamaalaykk mukalilulla oru nischitha aakruthiyilulla semi staanderd yuva taablokkukalude koottam upayogichu paaraameettar cheiyunnu...,). ithu inavariyant sidhaanthathinu pradhana prathyaaghaathangal undaakkunnu, ithu graasmaaniyante ekeekritha coordinate ringle hodginte pravartthanatthil ninnu aarambhich, dii konsini, processi, isenbood ennee sahakarikalumaayi jian-carlo rotta kooduthal paryavekshanam cheythu. chila vakra semi staanderd tabloxinte adisthaanathil vivarikkunna (mattu karyangalkkoppam) irreducible gadakangalaayi irreducible praathinidhyangalude tensor uthppannangalude vighadanam roopappeduthunnu.
beejaganita jyaamithiyilekkulla prayogangal grassmanian, flag enangal ennivayile shubert calculusine chuttippattiyaan. chila pradhana cohomology klaasukale shubert polynomialukal prathinidheekarikkukayum yuva taablokalude adisthaanathil vivarikkukayum cheyyaam.
praathinidhya sidhaanthathile prayogangal.
sankeernna samkhyakalkku mukalilulla samamiti grouppinte irreducible praathinidyangalumaayi parasparam bandhappettaan yuva rekhaachitrangal. irreducible praathinidyangal nirmmikkunna yuva simetrisarukal vyakthamaakkunnathinulla soukaryapradamaaya maarggam avaa nalkunnu. oru praathinidhyathekkurichu niravadhi vasthuthakal anubandha rekhaachithrathil ninnu oohikkaan kazhiyum. thaazhe, njangal rund udaaharanagal vivarikkunnu oru praathinidhyatthinte alavum niyantritha praathinidyangalum nirnnayikkuka. rund saahacharyangalilum, oru praathinidhyatthinte chila gunangal athinte rekhaachithram upayogichu nirnnayikkaan kazhiyumennu namukk kaanam. yuva tablos cemetric grouppinte upayogathil ulppedunnu
attangal, thanmathrakal, kharapadaarthangal ennivayekkurichulla kwaandam rasatantra patanam.
yuva rekhaachitrangal pothuvaaya rekheeya grouppinte irreducible polynomial praathinidyangal (avaykku mikkavarum shoonyamallaatha varikal ullappol), allengil prathyeka rekheeya grouppinte irreducible praathinidyangal (avaykku ettavum shoonyamallaatha varikal ullappol), allengil prathyeka eakaathmaka grouppinte irreducible sankeernna praathinidyangal (avaykku ettavum shoonyamallaatha varikal ullappol) enniva paaraameettar cheiyunnu. eee sandarbhangalil, saadhaarana taablokkukalallathe, oru pradhana punk vahikkunnathinulla entrikal ulla semi staanderd taablokkukal; prathyekichu aaa taablokkukalude ennamaanu praathinidhyatthinte alavu nirnnayikkunnath.
oru praathinidhyatthinte alavu.
oru partition anusarichulla cemetric grouppinte irreducible praathinidhyatthinte alavu praathinidhyatthinte rekhaachithrathil ninnu nedaan kazhiyunna vyathyastha staanderd yuva taablokkukalude ennathinu thulyamaanu. hook length formula upayogichu eee samkhya kanakkakkaam.
aakruthiyilulla oru boxinte oru hook neelam, athinte valathuvashathulla ore variyil athe nirayilulla boxukaludeyum athinu thaazheyulla athe nirayilulla boxukaludeyum ennavum, koodaathe orennavum (boxinu thanne) aanu. hook-length formula anusarichu, oru irreducible praathinidhyatthinte alavine praathinidhyatthinte rekhaachithrathile ellah boxukaludeyum hook length uthppannam kondu harikkunnu
valathuvashathulla chithram 10 = 5 + 4 + 1 enna partition rekhaachithrathile ellah boxukaludeyum hook-neelam kaanikkunnu.
athupole, "n"-nte "λ" enna partition (paramavadhi "r" bhagangal ulla)-nuu anusrithamaayi irreducible praathinidhyatthinte alavu "λ" aakruthiyilulla ardhamaanamulla yuva taablokkukalude ennamaanu (1 muthal "r" vareyulla entrikal maathram adangiyirikkunnu), ithu hook-length formula nalkunnu
ivide soochika "i" oru boxinte variyum "j" oru nirayum nalkunnu. udaaharanathinu, partition (5,4,1)-nuu (varikal kondu boxukal sanjarikkunnathu) anubandha irreducible praathinidhyatthinte alavayi namukk labikkum
parimithamaaya praathinidyangal.
moolakangalile samamiti grouppinte praathinidhyam, moolakangalile samamiti grouppinte praathinidhyam koodiyaanu. ennirunnaalum, oru irreducible praathinidhyam irreducible aayirikkilla. pakaram, ithu irreducible aaya niravadhi praathinidhyangalude nerittulla thukayayirikkaam. eee praathinidhyangale niyantritha praathinidhyatthinte gadakangal ennu vilikkunnu (induced praathinidyavum kaanuka).
s" "n" enna oru partitionode poruthappedunna "s" "n" enna thannirikkunna irreducible praathinidhyatthinte niyantritha praathinidhyatthinte eee vighadanam nirnnayikkunnathinulla chodyathinu inipparayunna utharam nalkunnu. oru boxes maathram neekkam cheythukondu aakruthiyude rekhaachithrathil ninnu nedaan kazhiyunna ellah yuva rekhaachithrangaludeyum koottam onnu roopappeduthunnu (athu athinte variyudeyum nirayudeyum avasaanathilaayirikkanam); niyantritha praathinidhyam aaa rekhaachithrangalumaayi poruthappedunna irreducible praathinidhyangalude nerittulla thukayayi vighadikkunnu, oronnum thukayude krithyathayil orikkal sambhavikkunnu.

