"평면 분할 (plane partitions)"의 두 판 사이의 차이
Pythagoras0 (토론 | 기여) (→생성함수) |
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| (같은 사용자의 중간 판 6개는 보이지 않습니다) | |||
| 4번째 줄: | 4번째 줄: | ||
==평면분할의 예== | ==평면분할의 예== | ||
===2의 평면분할 목록=== | ===2의 평면분할 목록=== | ||
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\left\{ \begin{array}{l} \{2\} \end{array} , \begin{array}{l} \{1,1\} \end{array} , \begin{array}{l} \{1\} \\ \{1\} \end{array} \right\} | \left\{ \begin{array}{l} \{2\} \end{array} , \begin{array}{l} \{1,1\} \end{array} , \begin{array}{l} \{1\} \\ \{1\} \end{array} \right\} | ||
| − | + | </math> | |
===3의 평면분할=== | ===3의 평면분할=== | ||
| − | + | :<math> | |
\left\{ \begin{array}{l} \{3\} \end{array} , \begin{array}{l} \{2,1\} \end{array} , \begin{array}{l} \{1,1,1\} \end{array} , \begin{array}{l} \{2\} \\ \{1\} \end{array} , \begin{array}{l} \{1,1\} \\ \{1\} \end{array} , \begin{array}{l} \{1\} \\ \{1\} \\ \{1\} \end{array} \right\} | \left\{ \begin{array}{l} \{3\} \end{array} , \begin{array}{l} \{2,1\} \end{array} , \begin{array}{l} \{1,1,1\} \end{array} , \begin{array}{l} \{2\} \\ \{1\} \end{array} , \begin{array}{l} \{1,1\} \\ \{1\} \end{array} , \begin{array}{l} \{1\} \\ \{1\} \\ \{1\} \end{array} \right\} | ||
| − | + | </math> | |
===4의 평면분할=== | ===4의 평면분할=== | ||
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\left\{ | \left\{ | ||
\begin{array}{c} | \begin{array}{c} | ||
| 81번째 줄: | 81번째 줄: | ||
\end{array} | \end{array} | ||
\right\} | \right\} | ||
| − | + | </math> | |
| 93번째 줄: | 93번째 줄: | ||
\end{aligned} | \end{aligned} | ||
</math> | </math> | ||
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==메모== | ==메모== | ||
| 111번째 줄: | 100번째 줄: | ||
* Math Overflow http://mathoverflow.net/search?q= | * Math Overflow http://mathoverflow.net/search?q= | ||
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==관련된 항목들== | ==관련된 항목들== | ||
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==매스매티카 파일 및 계산 리소스== | ==매스매티카 파일 및 계산 리소스== | ||
| 126번째 줄: | 115번째 줄: | ||
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| − | ==사전 | + | ==사전 형태의 자료== |
* http://en.wikipedia.org/wiki/Plane_partition | * http://en.wikipedia.org/wiki/Plane_partition | ||
| 138번째 줄: | 127번째 줄: | ||
==관련논문== | ==관련논문== | ||
| + | * Andrij Rovenchak, Statistical mechanics approach in the counting of integer partitions, http://arxiv.org/abs/1603.01049v1 | ||
| + | * Kamioka, Shuhei. “Plane Partitions with Bounded Size of Parts and Biorthogonal Polynomials.” arXiv:1508.01674 [math], August 7, 2015. http://arxiv.org/abs/1508.01674. | ||
* Gessel, Ira M. “A Historical Survey of P-Partitions.” arXiv:1506.03508 [math], June 10, 2015. http://arxiv.org/abs/1506.03508. | * Gessel, Ira M. “A Historical Survey of P-Partitions.” arXiv:1506.03508 [math], June 10, 2015. http://arxiv.org/abs/1506.03508. | ||
* Ciucu, Mihai. ‘Four Factorization Formulas for Plane Partitions’. arXiv:1503.07915 [cond-Mat], 26 March 2015. http://arxiv.org/abs/1503.07915. | * Ciucu, Mihai. ‘Four Factorization Formulas for Plane Partitions’. arXiv:1503.07915 [cond-Mat], 26 March 2015. http://arxiv.org/abs/1503.07915. | ||
* Destainville, Nicolas, and Suresh Govindarajan. 2014. “Estimating the Asymptotics of Solid Partitions.” arXiv:1406.5605 [cond-Mat, Physics:hep-Th], June. http://arxiv.org/abs/1406.5605. | * Destainville, Nicolas, and Suresh Govindarajan. 2014. “Estimating the Asymptotics of Solid Partitions.” arXiv:1406.5605 [cond-Mat, Physics:hep-Th], June. http://arxiv.org/abs/1406.5605. | ||
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[[분류:q-급수]] | [[분류:q-급수]] | ||
[[분류:분할수]] | [[분류:분할수]] | ||
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| + | ==메타데이터== | ||
| + | ===위키데이터=== | ||
| + | * ID : [https://www.wikidata.org/wiki/Q7201015 Q7201015] | ||
| + | ===Spacy 패턴 목록=== | ||
| + | * [{'LOWER': 'plane'}, {'LEMMA': 'partition'}] | ||
2021년 2월 17일 (수) 06:06 기준 최신판
개요
평면분할의 예
2의 평면분할 목록
\[ \left\{ \begin{array}{l} \{2\} \end{array} , \begin{array}{l} \{1,1\} \end{array} , \begin{array}{l} \{1\} \\ \{1\} \end{array} \right\} \]
3의 평면분할
\[ \left\{ \begin{array}{l} \{3\} \end{array} , \begin{array}{l} \{2,1\} \end{array} , \begin{array}{l} \{1,1,1\} \end{array} , \begin{array}{l} \{2\} \\ \{1\} \end{array} , \begin{array}{l} \{1,1\} \\ \{1\} \end{array} , \begin{array}{l} \{1\} \\ \{1\} \\ \{1\} \end{array} \right\} \]
4의 평면분할
\[ \left\{ \begin{array}{c} \{4\} \\ \end{array} , \begin{array}{c} \{2,2\} \\ \end{array} , \begin{array}{c} \{3,1\} \\ \end{array} , \begin{array}{c} \{2,1,1\} \\ \end{array} , \begin{array}{c} \{1,1,1,1\} \\ \end{array} , \begin{array}{c} \{2\} \\ \{2\} \\ \end{array} , \begin{array}{c} \{3\} \\ \{1\} \\ \end{array} , \begin{array}{c} \{1,1\} \\ \{1,1\} \\ \end{array} , \begin{array}{c} \{2,1\} \\ \{1\} \\ \end{array} , \begin{array}{c} \{1,1,1\} \\ \{1\} \\ \end{array} , \begin{array}{c} \{2\} \\ \{1\} \\ \{1\} \\ \end{array} , \begin{array}{c} \{1,1\} \\ \{1\} \\ \{1\} \\ \end{array} , \begin{array}{c} \{1\} \\ \{1\} \\ \{1\} \\ \{1\} \\ \end{array} \right\} \]
생성함수
- 다음과 같이 무한곱으로 표현가능하다
\[ \begin{aligned} \sum_{\pi:\text{plane partitions}}q^{|\pi|} & = \prod_{n=1}^\infty \frac {1}{(1-q^n)^n} \\ & =1 + q + 3 q^2 + 6 q^3 + 13 q^4 + 24 q^5 + 48 q^6 + 86 q^7 + 160 q^8 + 282 q^9 + 500 q^{10}+\cdots \end{aligned} \]
메모
관련된 항목들
매스매티카 파일 및 계산 리소스
사전 형태의 자료
리뷰, 에세이, 강의노트
- Krattenthaler, C. ‘Plane Partitions in the Work of Richard Stanley and His School’. arXiv:1503.05934 [math], 19 March 2015. http://arxiv.org/abs/1503.05934.
관련논문
- Andrij Rovenchak, Statistical mechanics approach in the counting of integer partitions, http://arxiv.org/abs/1603.01049v1
- Kamioka, Shuhei. “Plane Partitions with Bounded Size of Parts and Biorthogonal Polynomials.” arXiv:1508.01674 [math], August 7, 2015. http://arxiv.org/abs/1508.01674.
- Gessel, Ira M. “A Historical Survey of P-Partitions.” arXiv:1506.03508 [math], June 10, 2015. http://arxiv.org/abs/1506.03508.
- Ciucu, Mihai. ‘Four Factorization Formulas for Plane Partitions’. arXiv:1503.07915 [cond-Mat], 26 March 2015. http://arxiv.org/abs/1503.07915.
- Destainville, Nicolas, and Suresh Govindarajan. 2014. “Estimating the Asymptotics of Solid Partitions.” arXiv:1406.5605 [cond-Mat, Physics:hep-Th], June. http://arxiv.org/abs/1406.5605.
메타데이터
위키데이터
- ID : Q7201015
Spacy 패턴 목록
- [{'LOWER': 'plane'}, {'LEMMA': 'partition'}]