"Q-이항계수의 목록"의 두 판 사이의 차이

2011년 5월 13일 (금) 05:04 판

이 항목의 스프링노트 원문주소

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}

재미있는 사실

네이버 지식인 http://kin.search.naver.com/search.naver?where=kin_qna&query=

역사

수학사연표

@@ 6번째 줄: / 6번째 줄: @@
 <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>
+*  정의<br><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><br>
@@ 13번째 줄: / 15번째 줄: @@
 <h5 style="margin: 0px; line-height: 2em;">목록</h5>
-*  다음 목록은 <math>n</math> 과 <math>r=0,1,\cdots,n</math>에 대한 q-이항계수<br><math>n=1, \{{1,1}\}</math><br><math>n=2, \{{1,1+q,1}\}</math><br><math>n=3, \{{1,1+q+q^2,1+q+q^2,1}\}</math><br><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><br><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><br>
+*  다음 목록은 자연수 <math>n</math> 과 <math>r=0,1,\cdots,n</math>에 대한 q-이항계수<br><math>n=1, \{{1,1}\}</math><br><math>n=2, \{{1,1+q,1}\}</math><br><math>n=3, \{{1,1+q+q^2,1+q+q^2,1}\}</math><br><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><br><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><br> 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}<br> 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}<br> 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}<br> 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}<br> 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}<br>
@@ 40번째 줄: / 40번째 줄: @@
 <h5>메모</h5>
-<h5>관련된 항목들</h5>
-<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>
-* http://www.google.com/dictionary?langpair=en|ko&q=
-* [http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집]<br>
-** http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=
-* [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]
-<h5>사전 형태의 자료</h5>
-* http://ko.wikipedia.org/wiki/
-* http://en.wikipedia.org/wiki/
-* http://www.wolframalpha.com/input/?i=
-* [http://dlmf.nist.gov/ NIST Digital Library of Mathematical Functions]
-* [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences]<br>
-** http://www.research.att.com/~njas/sequences/?q=
-<h5>관련논문</h5>
-* http://www.jstor.org/action/doBasicSearch?Query=
-* http://dx.doi.org/
-<h5>관련도서 및 추천도서</h5>
-*  도서내검색<br>
-** http://books.google.com/books?q=
-** http://book.daum.net/search/contentSearch.do?query=
-*  도서검색<br>
-** http://books.google.com/books?q=
-** http://book.daum.net/search/mainSearch.do?query=
-** http://book.daum.net/search/mainSearch.do?query=
-<h5>관련기사</h5>
-*  네이버 뉴스 검색 (키워드 수정)<br>
-** http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
-** http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
-** http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
-<h5>블로그</h5>
-*  구글 블로그 검색<br>
-** http://blogsearch.google.com/blogsearch?q=
-* [http://navercast.naver.com/science/list 네이버 오늘의과학]
-* [http://math.dongascience.com/ 수학동아]
-* [http://www.ams.org/mathmoments/ Mathematical Moments from the AMS]
-* [http://betterexplained.com/ BetterExplained]

"Q-이항계수의 목록"의 두 판 사이의 차이

2011년 5월 13일 (금) 05:04 판

목차

이 항목의 스프링노트 원문주소

개요

목록

재미있는 사실

역사

메모

둘러보기 메뉴

검색