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A180349 Gog words avoiding the subpattern 312 0

%I #11 Mar 31 2012 10:24:26

%S 1,2,6,26,162,1450,18626,343210,9069306,343611106,18662952122,

%T 1453016097506

%N Gog words avoiding the subpattern 312

%C Gog words of size n are words of length n in an alphabet

%C of odd-sized tuples of increasing integers

%C that satisfy the following conditions:

%C (1) The length of the word is n,

%C (2) Each letter in the word has maximum entry at most n,

%C (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,

%C (4) Every repeated integer alternates in odd and even numbered positions in subsequent tuples.

%C They are in natural bijection with alternating sign matrices.

%C 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

%C (1) c, a, b appear in odd positions in x_i, x_j , x_k respectively where i<j<k,

%C (2) b is not in an even position in x_{i+1},..., x_{k-1},

%C (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.

%C (4) a < b < c.

%H Arvind Ayyer, Robert Cori, Dominique Gouyou-Beauchamps,

%H <a href="http://arxiv.org/abs/1101.1666">Monotone triangles and 312 pattern avoidance</a>, arXiv:1101.1666

%e For n=3, there are 7 gog words - (1)(2)(3), (1)(3)(2), (2)(1)(3), (2)(3)(1), (3)(1)(2), (3)(2)(1) and (2)(123)(2). Of these, all but (3)(1)(2) avoid the subpattern 312.

%e More complicated examples: 31(234)3 and 25(12356)542 contain the subpattern 312 but 25(12456)532 does not.

%Y Cf. A005130, A000108, A116715, A116722, A116735

%K nonn,hard

%O 1,2

%A _Arvind Ayyer_, Jan 18 2011

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)