"Alternating sign matrix theorem"의 두 판 사이의 차이
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imported>Pythagoras0 |
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| 131번째 줄: | 131번째 줄: | ||
* [http://www.math.lsa.umich.edu/%7Elserrano/asm.pdf http://www.math.lsa.umich.edu/~lserrano/asm.pdf] | * [http://www.math.lsa.umich.edu/%7Elserrano/asm.pdf http://www.math.lsa.umich.edu/~lserrano/asm.pdf] | ||
* Propp, James. 2002. The many faces of alternating-sign matrices. math/0208125 (August 15). http://arxiv.org/abs/math/0208125. | * Propp, James. 2002. The many faces of alternating-sign matrices. math/0208125 (August 15). http://arxiv.org/abs/math/0208125. | ||
| − | * How the alternating sign matrix conjecture was solved, | + | * How the alternating sign matrix conjecture was solved, |
** Bressoud, David M. and Propp, James, | ** Bressoud, David M. and Propp, James, | ||
** Notices of the American Mathematical Society, 46 (1999), 637-646. | ** Notices of the American Mathematical Society, 46 (1999), 637-646. | ||
| − | * Another proof of the alternating sign matrix conjecture | + | * Another proof of the alternating sign matrix conjecture |
** G Kuperberg, International Mathematics Research Notes (1996), 139-150. | ** G Kuperberg, International Mathematics Research Notes (1996), 139-150. | ||
| − | * Proof of the alternating sign matrix conjecture | + | * Proof of the alternating sign matrix conjecture |
** Zeilberger, Doron | ** Zeilberger, Doron | ||
** Electronic Journal of Combinatorics 3 (1996), R13. | ** Electronic Journal of Combinatorics 3 (1996), R13. | ||
| − | * [http://www.springerlink.com/content/tkg425gj56837471/ Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions. Disordered Phase] | + | * [http://www.springerlink.com/content/tkg425gj56837471/ Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions. Disordered Phase] |
** Bleher, Pavel M.; Fokin, Vladimir V. | ** Bleher, Pavel M.; Fokin, Vladimir V. | ||
2020년 11월 16일 (월) 03:15 판
introduction
- descending plane partitions and alternating sign matrix [1]http://math.berkeley.edu/~reshetik/RTG-semin-fall-2010/Philippe.pdf[2]
- Refined enumeration of Alternating Sign Matrices and Descending Plane Partitions
lambda-determinant
ASM
DPP
- http://mathworld.wolfram.com/DescendingPlanePartition.html
- number of DPPs with parts at most n is given by Andrews in 1979.
- number of ASM of size n is same as the above sequence
DPP to lattice paths
- P. Lalonde, Lattice paths and the antiautomorphism of the poset of descending plane partitions, Discrete Math. 271 (2003) 311–319
- Descending plane partitions and rhombus tilings of a hexagon with a triangular hole C. Krattenthaler, 2006
- Rhombus tilings/Dimers or Lattice Paths for DPPs
- lattice paths (lattice fermions)
- related to non-intersecting paths
- Gessel-Viennot theorem
from ASM to 6 vertex model with domain wall boundary condition(6VDW)
- Kuperberg
- Izergin - Korepin
1+1 dimensional Lorentzian quantum gravity
exists quantities \phi such that if \phi(g,a)=\phi'(g',a') then [T(a,g),T(a',g')]=0
\phi(g,a)=\frac{1-g^2(1-a^2)}{ag}=q+q^{-1}
history
- 1983 Mills, Robbins and Rumsey ASM conjecture
- 198? Korepin recurrence relation for 6VDW
- 1987 Izergin. determinant function of the partition function of the 6VDW based on Korepin's work
- 1996 Zilberger proof of ASM conjecture
- 1996 Kuperberg alternative proof of ASM conjecture using the connection with the six vertex model
- 2011 correspondence between DPP and ASM
- http://www.google.com/search?hl=en&tbs=tl:1&q=
computational resource
encyclopedia
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/Plane_partition
- http://en.wikipedia.org/wiki/alternating_sign_matrix
- http://en.wikipedia.org/wiki/Six-vertex_model
books
- 찾아볼 수학책
- R. J. Baxter Exactly Solved Models in Statistical mechanics
- Proofs and Confirmations
- Bressoud, David M.,
- MAA Spectrum, Mathematical Associations of America, Washington, D.C., 1999.
- Proofs and Confirmation
expositions
- http://www.macalester.edu/~bressoud/talks/
- http://www.macalester.edu/~bressoud/talks/2009/asm-Moravian.pdf
articles
- http://arxiv.org/abs/1512.06030
- http://www.math.lsa.umich.edu/~lserrano/asm.pdf
- Propp, James. 2002. The many faces of alternating-sign matrices. math/0208125 (August 15). http://arxiv.org/abs/math/0208125.
- How the alternating sign matrix conjecture was solved,
- Bressoud, David M. and Propp, James,
- Notices of the American Mathematical Society, 46 (1999), 637-646.
- Another proof of the alternating sign matrix conjecture
- G Kuperberg, International Mathematics Research Notes (1996), 139-150.
- Proof of the alternating sign matrix conjecture
- Zeilberger, Doron
- Electronic Journal of Combinatorics 3 (1996), R13.
- Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions. Disordered Phase
- Bleher, Pavel M.; Fokin, Vladimir V.