STATUS
proposed
approved
The OEIS is supported by the many generous donors to the OEIS Foundation.
Revision History for A048601
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
Robbins triangle read by rows: T(n,k) = number of alternating sign n X n matrices with a 1 at top of column k (n >= 1, 1<=k<=n)
(history; published version)
(history; published version)
STATUS
editing
proposed
COMMENTS
Named after the American mathematician David Peter Robbins (1942-2003). - Amiram Eldar, Jun 13 2021
REFERENCES
D. David Bressoud, Proofs and Confirmations: The Story of the Alternating Sign Matrix Conjecture, Cambridge University Press, 1999, p. 5.
LINKS
R. Roger E. Behrend, P. Philippe Di Francesco, P. and Paul Zinn-Justin, <a href="http://arxiv.org/abs/1103.1176">On the weighted enumeration of Alternating Sign Matrices and Descending Plane Partitions</a>, arXiv:1103.1176 [math.CO], 2011.
D. M. David Bressoud and J. James Propp, <a href="http://www.ams.org/notices/199906/fea-bressoud.pdf">How the alternating sign matrix conjecture was solved</a>, Notices Amer. Math. Soc., Vol. 46 (, No. 6, (1999), p. 637-646.
FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/StatisticsDatabase/St000066">The column of the unique '1' in the first row of the alternating sign matrix.</a>.
FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/St000066/">The column of the unique 1 in the first row of the alternating sign matrix.</a>.
W. H. Mills, David P . Robbins, and Howard Rumsey , Jr., <a href="http://dx.doi.org/10.1016/0097-3165(83)90068-7">Alternating sign matrices and descending plane partitions</a> J. Combin. Theory , Ser. A , Vol. 34 , No. 3 (1983), nopp. 3, 340--359. MR0700040 (85b:05013).
Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AlternatingSignMatrix.html">Alternating Sign Matrix.</a>.
D. Doron Zeilberger, <a href="http://arXiv.org/abs/math.CO/9606224">Proof of the Refined Alternating Sign Matrix Conjecture</a>, arXiv:math/9606224 [math.CO], 1996.
D. Doron Zeilberger, <a href="http://www.math.rutgers.edu/~zeilberg/DaveRobbins/guess.html">Dave Robbins's Art of Guessing</a>, Adv. in Appl. Math. , Vol. 34 (2005), pp. 939-954.
STATUS
approved
editing
STATUS
proposed
approved
STATUS
editing
proposed
EXAMPLE
1,
1, 1,
2, 3, 2,
7, 14, 14, 7,
42, 105, 135, 105, 42,
429, 1287, 2002, 2002, 1287, 429,
7436, 26026, 47320, 56784, 47320, 26026, 7436,
...
...
AUTHOR
STATUS
approved
editing
STATUS
proposed
approved
STATUS
editing
proposed
LINKS
P. Di Francesco, <a href="http://arXiv.org/abs/cond-mat/0409576">A refined Razumov-Stroganov conjecture II</a>, arXiv:cond-mat/0409576 [cond-mat.stat-mech], 2004.
LINKS
P. Di Francesco, <a href="http://arXiv.org/abs/cond-mat/0409576">A refined Razumov-Stroganov conjecture II</a>
P. Di Francesco, <a href="http://arXiv.org/abs/cond-mat/0409576">A refined Razumov-Stroganov conjecture II</a>
STATUS
proposed
editing