"Q-이항계수의 목록"의 두 판 사이의 차이

수학노트
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(사용자 2명의 중간 판 12개는 보이지 않습니다)
1번째 줄: 1번째 줄:
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<h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">이 항목의 스프링노트 원문주소</h5>
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==개요==
  
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*  정의:<math>{n \choose r}_q={{[n]_q!} \over {[r]_q![n - r]_q!}}=\frac{(q;q)_n}{(q;q)_r(q;q)_{n-r}}=\frac{(1-q)_q^n}{(1-q)_q^r (1-q)_q^{n-r}}</math>
  
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<h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">개요</h5>
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==목록==
  
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*  다음 목록은 자연수 <math>n</math> 과 <math>r=0,1,\cdots,n</math>에 대한 q-이항계수:<math>n=1, \{{1,1}\}</math>:<math>n=2, \{{1,1+q,1}\}</math>:<math>n=3, \{{1,1+q+q^2,1+q+q^2,1}\}</math>:<math>n=4, \{{1,1+q+q^2+q^3,(1+q^2) (1+q+q^2),1+q+q^2+q^3,1}\}</math>:<math>n=5, \{{1,1+q+q^2+q^3+q^4,(1+q^2) (1+q+q^2+q^3+q^4),(1+q^2) (1+q+q^2+q^3+q^4),1+q+q^2+q^3+q^4,1}\}</math> n=6,{1,1+q+q^2+q^3+q^4+q^5,(1+q^2+q^4) (1+q+q^2+q^3+q^4),(1+q^2) (1+q^3) (1+q+q^2+q^3+q^4),(1+q^2+q^4) (1+q+q^2+q^3+q^4),1+q+q^2+q^3+q^4+q^5,1} n=7,{1,1+q+q^2+q^3+q^4+q^5+q^6,(1+q^2+q^4) (1+q+q^2+q^3+q^4+q^5+q^6),(1-q+q^2) (1+q+q^2+q^3+q^4) (1+q+q^2+q^3+q^4+q^5+q^6),(1-q+q^2) (1+q+q^2+q^3+q^4) (1+q+q^2+q^3+q^4+q^5+q^6),(1+q^2+q^4) (1+q+q^2+q^3+q^4+q^5+q^6),1+q+q^2+q^3+q^4+q^5+q^6,1} n=8,{1,1+q+q^2+q^3+q^4+q^5+q^6+q^7,(1+q^2+q^4+q^6) (1+q+q^2+q^3+q^4+q^5+q^6),(1-q+q^2) (1+q+q^2+q^3+q^4+q^5+q^6) (1+q+q^2+q^3+q^4+q^5+q^6+q^7),(1-q+q^2) (1+q^4) (1+q+q^2+q^3+q^4) (1+q+q^2+q^3+q^4+q^5+q^6),(1-q+q^2) (1+q+q^2+q^3+q^4+q^5+q^6) (1+q+q^2+q^3+q^4+q^5+q^6+q^7),(1+q^2+q^4+q^6) (1+q+q^2+q^3+q^4+q^5+q^6),1+q+q^2+q^3+q^4+q^5+q^6+q^7,1} n=9,{1,1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8,(1+q^2+q^4+q^6) (1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8),(1+q^3+q^6) (1+q^2+q^4+q^6) (1+q+q^2+q^3+q^4+q^5+q^6),(1-q+q^2) (1+q^4) (1+q+q^2+q^3+q^4+q^5+q^6) (1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8),(1-q+q^2) (1+q^4) (1+q+q^2+q^3+q^4+q^5+q^6) (1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8),(1+q^3+q^6) (1+q^2+q^4+q^6) (1+q+q^2+q^3+q^4+q^5+q^6),(1+q^2+q^4+q^6) (1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8),1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8,1} n=10,{1,1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8+q^9,(1+q^2+q^4+q^6+q^8) (1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8),(1+q^3+q^6) (1+q^2+q^4+q^6) (1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8+q^9),(1+q^4) (1+q^3+q^6) (1+q+q^2+q^3+q^4+q^5+q^6) (1+q^2+q^4+q^6+q^8),(1+q) (1-q+q^2) (1+q+q^2) (1+q^4) (1-q+q^2-q^3+q^4) (1+q^3+q^6) (1+q+q^2+q^3+q^4+q^5+q^6),(1+q^4) (1+q^3+q^6) (1+q+q^2+q^3+q^4+q^5+q^6) (1+q^2+q^4+q^6+q^8),(1+q^3+q^6) (1+q^2+q^4+q^6) (1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8+q^9),(1+q^2+q^4+q^6+q^8) (1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8),1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8+q^9,1}
  
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<h5 style="margin: 0px; line-height: 2em;">목록</h5>
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<math>n=1,{1,1} n=2,{1,1+q,1} n=3,{1,1+q+q^2,1+q+q^2,1} n=4,{1,1+q+q^2+q^3,(1+q^2) (1+q+q^2),1+q+q^2+q^3,1} n=5,{1,1+q+q^2+q^3+q^4,(1+q^2) (1+q+q^2+q^3+q^4),(1+q^2) (1+q+q^2+q^3+q^4),1+q+q^2+q^3+q^4,1} n=6,{1,1+q+q^2+q^3+q^4+q^5,(1+q^2+q^4) (1+q+q^2+q^3+q^4),(1+q^2) (1+q^3) (1+q+q^2+q^3+q^4),(1+q^2+q^4) (1+q+q^2+q^3+q^4),1+q+q^2+q^3+q^4+q^5,1} n=7,{1,1+q+q^2+q^3+q^4+q^5+q^6,(1+q^2+q^4) (1+q+q^2+q^3+q^4+q^5+q^6),(1-q+q^2) (1+q+q^2+q^3+q^4) (1+q+q^2+q^3+q^4+q^5+q^6),(1-q+q^2) (1+q+q^2+q^3+q^4) (1+q+q^2+q^3+q^4+q^5+q^6),(1+q^2+q^4) (1+q+q^2+q^3+q^4+q^5+q^6),1+q+q^2+q^3+q^4+q^5+q^6,1} n=8,{1,1+q+q^2+q^3+q^4+q^5+q^6+q^7,(1+q^2+q^4+q^6) (1+q+q^2+q^3+q^4+q^5+q^6),(1-q+q^2) (1+q+q^2+q^3+q^4+q^5+q^6) (1+q+q^2+q^3+q^4+q^5+q^6+q^7),(1-q+q^2) (1+q^4) (1+q+q^2+q^3+q^4) (1+q+q^2+q^3+q^4+q^5+q^6),(1-q+q^2) (1+q+q^2+q^3+q^4+q^5+q^6) (1+q+q^2+q^3+q^4+q^5+q^6+q^7),(1+q^2+q^4+q^6) (1+q+q^2+q^3+q^4+q^5+q^6),1+q+q^2+q^3+q^4+q^5+q^6+q^7,1} n=9,{1,1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8,(1+q^2+q^4+q^6) (1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8),(1+q^3+q^6) (1+q^2+q^4+q^6) (1+q+q^2+q^3+q^4+q^5+q^6),(1-q+q^2) (1+q^4) (1+q+q^2+q^3+q^4+q^5+q^6) (1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8),(1-q+q^2) (1+q^4) (1+q+q^2+q^3+q^4+q^5+q^6) (1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8),(1+q^3+q^6) (1+q^2+q^4+q^6) (1+q+q^2+q^3+q^4+q^5+q^6),(1+q^2+q^4+q^6) (1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8),1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8,1} n=10,{1,1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8+q^9,(1+q^2+q^4+q^6+q^8) (1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8),(1+q^3+q^6) (1+q^2+q^4+q^6) (1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8+q^9),(1+q^4) (1+q^3+q^6) (1+q+q^2+q^3+q^4+q^5+q^6) (1+q^2+q^4+q^6+q^8),(1+q) (1-q+q^2) (1+q+q^2) (1+q^4) (1-q+q^2-q^3+q^4) (1+q^3+q^6) (1+q+q^2+q^3+q^4+q^5+q^6),(1+q^4) (1+q^3+q^6) (1+q+q^2+q^3+q^4+q^5+q^6) (1+q^2+q^4+q^6+q^8),(1+q^3+q^6) (1+q^2+q^4+q^6) (1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8+q^9),(1+q^2+q^4+q^6+q^8) (1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8),1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8+q^9,1}</math>
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==역사==
  
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* [[수학사 연표]]
  
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<h5>재미있는 사실</h5>
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==메모==
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[[분류:q-급수]]
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* 네이버 지식인 http://kin.search.naver.com/search.naver?where=kin_qna&query=
 
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<h5>역사</h5>
 
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* [[수학사연표 (역사)|수학사연표]]
 
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<h5>메모</h5>
 
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<h5>관련된 항목들</h5>
 
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<h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">수학용어번역</h5>
 
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* http://www.google.com/dictionary?langpair=en|ko&q=
 
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* [http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집]<br>
 
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** http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=
 
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* [http://kms.or.kr/home/kor/board/bulletin_list_subject.asp?bulletinid=%7BD6048897-56F9-43D7-8BB6-50B362D1243A%7D&boardname=%BC%F6%C7%D0%BF%EB%BE%EE%C5%E4%B7%D0%B9%E6&globalmenu=7&localmenu=4 대한수학회 수학용어한글화 게시판]
 
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<h5>사전 형태의 자료</h5>
 
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* http://ko.wikipedia.org/wiki/
 
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* http://en.wikipedia.org/wiki/
 
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* http://www.wolframalpha.com/input/?i=
 
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* [http://dlmf.nist.gov/ NIST Digital Library of Mathematical Functions]
 
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* [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences]<br>
 
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** http://www.research.att.com/~njas/sequences/?q=
 
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<h5>관련논문</h5>
 
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* http://www.jstor.org/action/doBasicSearch?Query=
 
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* http://dx.doi.org/
 
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<h5>관련도서 및 추천도서</h5>
 
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*  도서내검색<br>
 
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** http://books.google.com/books?q=
 
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** http://book.daum.net/search/contentSearch.do?query=
 
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*  도서검색<br>
 
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** http://books.google.com/books?q=
 
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** http://book.daum.net/search/mainSearch.do?query=
 
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** http://book.daum.net/search/mainSearch.do?query=
 
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<h5>관련기사</h5>
 
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*  네이버 뉴스 검색 (키워드 수정)<br>
 
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** http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
 
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** http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
 
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** http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
 
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<h5>블로그</h5>
 
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*  구글 블로그 검색<br>
 
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** http://blogsearch.google.com/blogsearch?q=
 
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* [http://navercast.naver.com/science/list 네이버 오늘의과학]
 
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* [http://math.dongascience.com/ 수학동아]
 
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* [http://www.ams.org/mathmoments/ Mathematical Moments from the AMS]
 
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* [http://betterexplained.com/ BetterExplained]
 

2020년 12월 28일 (월) 02:58 기준 최신판

개요

  • 정의\[{n \choose r}_q={{[n]_q!} \over {[r]_q![n - r]_q!}}=\frac{(q;q)_n}{(q;q)_r(q;q)_{n-r}}=\frac{(1-q)_q^n}{(1-q)_q^r (1-q)_q^{n-r}}\]



목록

  • 다음 목록은 자연수 \(n\) 과 \(r=0,1,\cdots,n\)에 대한 q-이항계수\[n=1, \{{1,1}\}\]\[n=2, \{{1,1+q,1}\}\]\[n=3, \{{1,1+q+q^2,1+q+q^2,1}\}\]\[n=4, \{{1,1+q+q^2+q^3,(1+q^2) (1+q+q^2),1+q+q^2+q^3,1}\}\]\[n=5, \{{1,1+q+q^2+q^3+q^4,(1+q^2) (1+q+q^2+q^3+q^4),(1+q^2) (1+q+q^2+q^3+q^4),1+q+q^2+q^3+q^4,1}\}\] n=6,{1,1+q+q^2+q^3+q^4+q^5,(1+q^2+q^4) (1+q+q^2+q^3+q^4),(1+q^2) (1+q^3) (1+q+q^2+q^3+q^4),(1+q^2+q^4) (1+q+q^2+q^3+q^4),1+q+q^2+q^3+q^4+q^5,1} n=7,{1,1+q+q^2+q^3+q^4+q^5+q^6,(1+q^2+q^4) (1+q+q^2+q^3+q^4+q^5+q^6),(1-q+q^2) (1+q+q^2+q^3+q^4) (1+q+q^2+q^3+q^4+q^5+q^6),(1-q+q^2) (1+q+q^2+q^3+q^4) (1+q+q^2+q^3+q^4+q^5+q^6),(1+q^2+q^4) (1+q+q^2+q^3+q^4+q^5+q^6),1+q+q^2+q^3+q^4+q^5+q^6,1} n=8,{1,1+q+q^2+q^3+q^4+q^5+q^6+q^7,(1+q^2+q^4+q^6) (1+q+q^2+q^3+q^4+q^5+q^6),(1-q+q^2) (1+q+q^2+q^3+q^4+q^5+q^6) (1+q+q^2+q^3+q^4+q^5+q^6+q^7),(1-q+q^2) (1+q^4) (1+q+q^2+q^3+q^4) (1+q+q^2+q^3+q^4+q^5+q^6),(1-q+q^2) (1+q+q^2+q^3+q^4+q^5+q^6) (1+q+q^2+q^3+q^4+q^5+q^6+q^7),(1+q^2+q^4+q^6) (1+q+q^2+q^3+q^4+q^5+q^6),1+q+q^2+q^3+q^4+q^5+q^6+q^7,1} n=9,{1,1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8,(1+q^2+q^4+q^6) (1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8),(1+q^3+q^6) (1+q^2+q^4+q^6) (1+q+q^2+q^3+q^4+q^5+q^6),(1-q+q^2) (1+q^4) (1+q+q^2+q^3+q^4+q^5+q^6) (1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8),(1-q+q^2) (1+q^4) (1+q+q^2+q^3+q^4+q^5+q^6) (1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8),(1+q^3+q^6) (1+q^2+q^4+q^6) (1+q+q^2+q^3+q^4+q^5+q^6),(1+q^2+q^4+q^6) (1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8),1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8,1} n=10,{1,1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8+q^9,(1+q^2+q^4+q^6+q^8) (1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8),(1+q^3+q^6) (1+q^2+q^4+q^6) (1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8+q^9),(1+q^4) (1+q^3+q^6) (1+q+q^2+q^3+q^4+q^5+q^6) (1+q^2+q^4+q^6+q^8),(1+q) (1-q+q^2) (1+q+q^2) (1+q^4) (1-q+q^2-q^3+q^4) (1+q^3+q^6) (1+q+q^2+q^3+q^4+q^5+q^6),(1+q^4) (1+q^3+q^6) (1+q+q^2+q^3+q^4+q^5+q^6) (1+q^2+q^4+q^6+q^8),(1+q^3+q^6) (1+q^2+q^4+q^6) (1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8+q^9),(1+q^2+q^4+q^6+q^8) (1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8),1+q+q^2+q^3+q^4+q^5+q^6+q^7+q^8+q^9,1}



역사



메모

원본 주소 "https://wiki.mathnt.net/index.php?title=Q-이항계수의_목록&oldid=47848"