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1. Definition & Example

The seven alternating sign matrices of size 3

http://www.findstat.org/Graphics/api/Cc0017_0_[[1,0,0],[0,1,0],[0,0,1]].png

http://www.findstat.org/Graphics/api/Cc0017_0_[[0,1,0],[1,0,0],[0,0,1]].png

http://www.findstat.org/Graphics/api/Cc0017_0_[[1,0,0],[0,0,1],[0,1,0]].png

http://www.findstat.org/Graphics/api/Cc0017_0_[[0,1,0],[1,-1,1],[0,1,0]].png

http://www.findstat.org/Graphics/api/Cc0017_0_[[0,0,1],[1,0,0],[0,1,0]].png

http://www.findstat.org/Graphics/api/Cc0017_0_[[0,1,0],[0,0,1],[1,0,0]].png

http://www.findstat.org/Graphics/api/Cc0017_0_[[0,0,1],[0,1,0],[1,0,0]].png

 [[1,0,0],[0,1,0],[0,0,1]] 

 [[0,1,0],[1,0,0],[0,0,1]] 

 [[1,0,0],[0,0,1],[0,1,0]] 

 [[0,1,0],[1,-1,1],[0,1,0]] 

 [[0,0,1],[1,0,0],[0,1,0]] 

 [[0,1,0],[0,0,1],[1,0,0]] 

 [[0,0,1],[0,1,0],[1,0,0]] 

2. Properties

3. Remarks

4. References

[ABF]   A. Ayyer, R. E. Behrend, I. Fischer, Extreme diagonally and antidiagonally symmetric alternating sign matrices of odd order, preprint arXiv:1611.03823 [math.CO].

[And79]   G. E. Andrews, Plane partitions (III): The weak Macdonald conjecture, Inventiones mathematicae 53.3 (1979).

[And94]   G. E. Andrews, Plane Partitions V: The TSSCPP Conjecture, Journal of Combinatorial Theory, Series A 66.1 (1994).

[Beh13]   R. E. Behrend, Multiply-refined enumeration of alternating sign matrices, Advances in Mathematics 245 (2013).

[BFK17]   R. E. Behrend, I. Fischer, M. Konvalinka, Diagonally and antidiagonally symmetric alternating sign matrices of odd order, Advances in Mathematics 315 (2017).

[BP99]   D. Bressoud, J. Propp, How the alternating sign matrix conjecture was solved, Notices of the AMS 46.6 (1999).

[CS11]   L. Cantini, A. Sportiello, Proof of the Razumov–Stroganov conjecture, Journal of Combinatorial Theory, Series A 118.5 (2011).

[EKLP92a]   N. Elkies, G. Kuperberg, M. Larsen, J. Propp, Alternating-sign matrices and domino tilings (Part I), Journal of Algebraic Combinatorics 1.2 (1992).

[EKLP92b]   N. Elkies, G. Kuperberg, M. Larsen, J. Propp, Alternating-sign matrices and domino tilings (Part II), Journal of Algebraic Combinatorics 1.3 (1992).

[Fis16]   I. Fischer, Short proof of the ASM theorem avoiding the six-vertex model, Journal of Combinatorial Theory, Series A 144 (2016).

[Kup96]   G. Kuperberg, Another proof of the alternative-sign matrix conjecture, International Mathematics Research Notices 1996.3 (1996).

[MRR83]   W. H. Mills, D. P. Robbins, H. Rumsey, Alternating sign matrices and descending plane partitions, Journal of Combinatorial Theory, Series A 34.3 (1983).

[MRR86]   W. H. Mills, D. P. Robbins, H. Rumsey, Self-complementary totally symmetric plane partitions, Journal of Combinatorial Theory, Series A 42.2 (1986).

[Rob]   D. P. Robbins, Symmetry classes of alternating sign matrices, preprint arXiv:math/0008045 [math.CO].

[Rob91]   D. P. Robbins, The Story of 1, 2, 7, 42, 7436,..., The Mathematical Intelligencer 13.2 (1991).

[RR86]   D. P. Robbins, H. Rumsey, Determinants and alternating sign matrices, Advances in Mathematics 62.2 (1986).

[Zei96a]   D. Zeilberger, Proof of the alternating sign matrix conjecture, Electronic Journal of Combinatorics 3 (1996), R13.

[Zei96b]   D. Zeilberger, Proof of the refined alternating sign matrix conjecture, New York Journal of Mathematics 2 (1996).

5. Sage examples

6. Technical information for database usage