Proof of the alternating sign matrix conjecture
نویسنده
چکیده
Gert Almkvist, Noga Alon, George Andrews, Anonymous, Dror Bar-Natan, Francois Bergeron, Nantel Bergeron, Gaurav Bhatnagar, Anders Björner, Jonathan Borwein, Mireille Bousquest-Mélou, Francesco Brenti, E. Rodney Canfield, William Chen, Chu Wenchang, Shaun Cooper, Kequan Ding, Charles Dunkl, Richard Ehrenborg, Leon Ehrenpreis, Shalosh B. Ekhad, Kimmo Eriksson, Dominique Foata, Omar Foda, Aviezri Fraenkel, Jane Friedman, Frank Garvan, George Gasper, Ron Graham, Andrew Granville, Eric Grinberg, Laurent Habsieger, Jim Haglund, Han Guo-Niu, Roger Howe, Warren Johnson, Gil Kalai, Viggo Kann, Marvin Knopp, Don Knuth, Christian Krattenthaler, Gilbert Labelle, Jacques Labelle, Jane Legrange, Pierre Leroux, Ethan Lewis, Daniel Loeb, John Majewicz, Steve Milne, John Noonan, Kathy O’Hara, Soichi Okada, Craig Orr, Sheldon Parnes, Peter Paule, Bob Proctor, Arun Ram, Marge Readdy, Amitai Regev, Jeff Remmel, Christoph Reutenauer, Bruce Reznick, Dave Robbins, Gian-Carlo Rota, Cecil Rousseau, Bruce Sagan, Bruno Salvy, Isabella Sheftel, Rodica Simion, R. Jamie Simpson, Richard Stanley, Dennis Stanton, Volker Strehl, Walt Stromquist, Bob Sulanke, X.Y. Sun, Sheila Sundaram, Raphaële Supper, Nobuki Takayama, Xavier G. Viennot, Michelle Wachs, Michael Werman, Herb Wilf, Celia Zeilberger, Hadas Zeilberger, Tamar Zeilberger, Li Zhang, Paul Zimmermann .
منابع مشابه
Three alternating sign matrix identities in search of bijective proofs
These are rich combinatorial objects with connections to many problems in algebraic combinatorics (see [2], [3], [12]). They also have many different representations. The representation that was used in Kuperberg’s proof of the counting function for alternating sign matrices [9] and Zeilberger’s proof of the refined alternating sign matrix conjecture [14] is the six-vertex model of statistical ...
متن کاملProof of the Refined Alternating Sign Matrix Conjecture
Mills, Robbins, and Rumsey conjectured, and Zeilberger proved, that the number of alternating sign matrices of order n equals A(n) := 1!4!7! · · · (3n − 2)! n!(n + 1)! · · · (2n − 1)! . Mills, Robbins, and Rumsey also made the stronger conjecture that the number of such matrices whose (unique) ‘1’ of the first row is at the rth column equals A(n) `n+r−2 n−1 ́`2n−1−r n−1 ́ `3n−2 n−1 ́ . Standing on...
متن کاملThe Book Review Column 4. Analysis of Algorithms:an Active Learning Approach 5 Further Reading 6 Opinion
The prices I provided this time are from amazon.com; however, the website www.bestbookbuys.com gives a range of prices from place to purchase books on the web. (amazon.com is usually not the cheapest, and its usually not even close.). Welcome to the Book Reviews Column. We hope to bring you at least two reviews of books every month. In this column four books are reviewed. 1. Proofs and Confirma...
متن کاملReview of Proofs and Confirmations : the story of the alternating sign matrix conjecture
This equation came to be known as the ASM conjecture, and computational verification of the first 20 cases made it practically certain to be correct. But a proof remained elusive, despite the simplicity of the conjecture and a good deal of effort from the community of algebraic combinatoricists. Doron Zeilberger finally announced a proof in 1992, but it was not until 1995 that all the gaps were...
متن کاملC&O 739 Essay A Proof of the Alternating Sign Matrix Conjecture Using the Yang-Baxter Equation
An alternating sign matrix [1] is a generalization of a permutation matrix. It consists of a matrix whose entries are 1, −1, and 0, and it satisfies the condition that in every row and column, the 1’s and −1’s alternate (possibly with 0’s in between) and the sum of the entries in every row or column is equal to 1 (so the permutation matrices are one type of these, in which there are no −1’s). F...
متن کاملAnother Proof of the Alternating-Sign Matrix Conjecture
Alternating sign matrices are related to a number of other combinatorial objects that, remarkably, are also enumerated or conjectured to be enumerated by ratios of progressions of factorials or staggered factorials [9], [11]. Zeilberger [13] recently proved Theorem 1 by establishing that ASMs are equinumerous with totally symmetric, self-complementary plane partitions, which were enumerated by ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Electr. J. Comb.
دوره 3 شماره
صفحات -
تاریخ انتشار 1996