A245902 -id:A245902 - cp's OEIS frontend

A245895 Number of labeled increasing binary trees on 2n-1 nodes whose breadth-first reading word avoids 312.

1, 2, 11, 96, 1093

Offset: 1

Manda Riehl, Aug 22 2014

The number of labeled increasing binary trees with an associated permutation avoiding 312 in the classical sense. The tree's permutation is found by recording the labels in the order in which they appear in a breadth-first search. (Note that a breadth-first search reading word is equivalent to reading the tree labels left to right by levels, starting with the root.)

In some cases, the same breadth-first search reading permutation can be found on differently shaped trees. This sequence gives the number of trees, not the number of permutations.

			When n=3, a(n)=11.  In the Links above we show the eleven labeled increasing binary trees on five nodes whose permutation avoids 312.

Manda Riehl, For n = 3: the 11 labeled trees on 5 nodes whose associated permutation avoids 312.

A245889 gives the number of unary-binary trees instead of binary trees. A245902 gives the number of permutations which avoid 312 that are breadth-first reading words on labeled increasing binary trees.

A245899 a(n) is the number of permutations avoiding 312 that can be realized on increasing unary-binary trees with n nodes.

Original entry on oeis.org

1, 1, 2, 3, 7, 14, 37, 80

Offset: 1

Manda Riehl, Aug 06 2014

The number of permutations avoiding 312 in the classical sense which can be realized as labels on an increasing unary-binary tree read in the order they appear in a breadth-first search. (Note that breadth-first search reading word is equivalent to reading the tree left to right by levels, starting with the root.)

In some cases, more than one tree results in the same breadth-first search reading word, but here we count the permutations, not the trees.

			For example, when n=4, a(n)=3. The permutations 1234, 1243, and 1324 all avoid 312 in the classical sense and occur as breadth-first search reading words on an increasing unary-binary tree with 4 nodes:
       1           1            1
      / \         / \          / \
     2   3       2   4        3   2
     |           |                |
     4           3                4

D. Levin, L. Pudwell, M. Riehl, A. Sandberg, Pattern Avoidance on k-ary Heaps, Slides of Talk, 2014.

A245902 appears to be the odd-indexed terms of this sequence.

Cf. A245889 (the number of increasing unary-binary trees whose breadth-first reading word avoids 312).

cp's OEIS Frontend

A245895 Number of labeled increasing binary trees on 2n-1 nodes whose breadth-first reading word avoids 312.

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