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 A211400 Rectangular array, read by upward diagonals: T(n,m) is the number of Young tableaux that can be realized as the ranks of the outer sums a_i + b_j where a = (a_1, ... a_n) and b = (b_1, ... b_m) are real monotone vectors in general position (all sums different). 2
 1, 1, 1, 1, 2, 1, 1, 5, 5, 1, 1, 14, 36, 14, 1, 1, 42, 295, 295, 42, 1, 1, 132, 2583, 6660, 2583, 132, 1, 1, 429, 23580 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Alternatively, that can be realized as the ranks of the outer products a_i b_j where a = (a_1, ... a_n) and b = (b_1, ... b_m) are real positive monotone vectors. The entries at T(2,n) and T(m,2) are Catalan numbers (A000108). The original version of this sequence was 1  1  1  1  1   1   1 ... 1  2  5 14 42 132 428 ... 1  5 24 77 ... 1 14 77 ... 1 42 ... ... but some of the later entries seem to be incorrect. - Robert J. Vanderbei, Jan 09 2015 LINKS C. Mallows, R. J. Vanderbei, Which Young Tableaux Can Represent an Outer Sum?, J. Int. Seq. 18 (2015) #15.9.1. Robert J. Vanderbei, Solutions for the 3 X 3 case Robert J. Vanderbei, Solutions for the 3 X 4 case Robert J. Vanderbei, Solutions for the 4 X 4 case EXAMPLE The vectors a = (0,2) and b = (0,4,5) give the outer sums 0  4  5  which have ranks  1  3  4 2  6  7                    2  5  6 which is one of the five 2 X 3 Young tableaux. One of the 18 3 X 3 tableaux that cannot be realized as a set of outer sums is  1  2  6     3  5  7     4  8  9. The array begins 1      1      1      1      1      1      1      1      1 ... 1      2      5     14     42    132    429   1430   4862 ... (A000108) 1      5     36    295   2583  23580 221680    ... (A255489) 1     14    295   6660    ... 1     42   2583    ... 1    132  23580    ... 1    429 221680    ... 1   1430   ... 1   4862   ... ... CROSSREFS Cf. A060854, A000108, A255489. Sequence in context: A306344 A128612 A284731 * A060854 A091378 A156045 Adjacent sequences:  A211397 A211398 A211399 * A211401 A211402 A211403 KEYWORD nonn,hard,more,tabl AUTHOR Colin Mallows, Feb 08 2013 EXTENSIONS Corrected and extended by Robert J. Vanderbei, Jan 09 2015 STATUS approved

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Last modified December 8 02:30 EST 2019. Contains 329850 sequences. (Running on oeis4.)