The Minimal sorting probabilities, and the champion pairs for Standard Young\ Tableau of shape, [n, n, n, n], for n from 1 to, 12 By Shalosh B. Ekhad The minimal sorting probability of Standard Young tableaux of shape, [2, 2, 2, 2], but where one of the cells is in the first row is , 2/7, and in floating point, 0.2857142857, and this happens with the pairs of cells, {[[1, 2], [2, 1]]} The minimal sorting probability of Standard Young tableaux of shape, [3, 3, 3, 3], but where one of the cells is in the first row is , 1/11, and in floating point, 0.09090909091, and this happens with the pairs of cells, {[[1, 2], [2, 1]]} The minimal sorting probability of Standard Young tableaux of shape, [4, 4, 4, 4], but where one of the cells is in the first row is , 0, and in floating point, 0., and this happens with the pairs of cells, { [[1, 2], [2, 1]], [[1, 3], [3, 1]], [[1, 4], [2, 3]], [[1, 4], [3, 2]], [[1, 4], [4, 1]]} The minimal sorting probability of Standard Young tableaux of shape, [5, 5, 5, 5], but where one of the cells is in the first row is , 1/19, and in floating point, 0.05263157895, and this happens with the pairs of cells, {[[1, 2], [2, 1]]} The minimal sorting probability of Standard Young tableaux of shape, [6, 6, 6, 6], but where one of the cells is in the first row is , 2/23, and in floating point, 0.08695652174, and this happens with the pairs of cells, {[[1, 2], [2, 1]]} The minimal sorting probability of Standard Young tableaux of shape, 11881 [7, 7, 7, 7], but where one of the cells is in the first row is , ------, 289731 and in floating point, 0.04100700305, and this happens with the pairs of cells, {[[1, 6], [3, 3]]} The minimal sorting probability of Standard Young tableaux of shape, 88773 [8, 8, 8, 8], but where one of the cells is in the first row is , -------, 1344005 and in floating point, 0.06605109356, and this happens with the pairs of cells, {[[1, 5], [3, 2]]} The minimal sorting probability of Standard Young tableaux of shape, [9, 9, 9, 9], but where one of the cells is in the first row is , 224626067 ----------, and in floating point, 0.08623935426, 2604681690 and this happens with the pairs of cells, {[[1, 7], [4, 2]], [[1, 8], [4, 3]]} The minimal sorting probability of Standard Young tableaux of shape, [10, 10, 10, 10], but where one of the cells is in the first row is , 196469528 ----------, and in floating point, 0.02038631923, 9637322253 and this happens with the pairs of cells, {[[1, 7], [2, 5]]} The minimal sorting probability of Standard Young tableaux of shape, [11, 11, 11, 11], but where one of the cells is in the first row is , 23939431 ----------, and in floating point, 0.02185012478, 1095619876 and this happens with the pairs of cells, {[[1, 6], [2, 4]]} The minimal sorting probability of Standard Young tableaux of shape, [12, 12, 12, 12], but where one of the cells is in the first row is , 300783304 -----------, and in floating point, 0.004402001825, 68328754959 and this happens with the pairs of cells, {[[1, 7], [3, 3]]} ------------------------------------- This took, 4535.910, seconds. ----------------------- This took, 4535.911, seconds.