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Gog words of size n are words of length n in an alphabet
of odd-sized tuples of increasing integers
that satisfy the following conditions:
(1) The length of the word is n,
(2) Each letter in the word has maximum entry at most n,
(3) An integer in an even numbered position in a tuple is repeated in another tuple to its left and to its right in odd numbered positions,
(4) Every repeated integer alternates in odd and even numbered positions in subsequent tuples.
They are in natural bijection with alternating sign matrices.
Further, the integers c, a, b form a 312-subpattern of the Gog word w = x_1 x_2 ... x_n if the following conditions hold
(1) c, a, b appear in odd positions in x_i, x_j , x_k respectively where i<j<k,
(2) b is not in an even position in x_{i+1},..., x_{k-1},
(3) If x_j = (p_1, q_1, . . . , p_{k-1}, q_{k-1}, p_k), either b>p_k or p_l < b < q_l for some l.
(4) a < b < c.
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