Baxter permutations¶
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sage.combinat.baxter_permutations.
BaxterPermutations
¶ The combinatorial class of Baxter permutations.
A Baxter permutation is a permutation avoiding the generalized permutation patterns \(2-41-3\) and \(3-14-2\). In other words, a permutation \(\sigma\) is a Baxter permutation if for any subword \(u := u_1u_2u_3u_4\) of \(\sigma\) such that the letters \(u_2\) and \(u_3\) are adjacent in \(\sigma\), the standardized version of \(u\) is neither \(2413\) nor \(3142\).
See [Gir2012] for a study of Baxter permutations.
INPUT:
n
– (default:None
) a nonnegative integer, the size of the permutations.
OUTPUT:
Return the combinatorial class of the Baxter permutations of size
n
ifn
is notNone
. Otherwise, return the combinatorial class of all Baxter permutations.EXAMPLES:
sage: BaxterPermutations(5) Baxter permutations of size 5 sage: BaxterPermutations() Baxter permutations
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sage.combinat.baxter_permutations.
BaxterPermutations_all
¶ The enumerated set of all Baxter permutations.
See
BaxterPermutations
for the definition of Baxter permutations.EXAMPLES:
sage: from sage.combinat.baxter_permutations import BaxterPermutations_all sage: BaxterPermutations_all() Baxter permutations
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sage.combinat.baxter_permutations.
BaxterPermutations_size
¶ The enumerated set of Baxter permutations of a given size.
See
BaxterPermutations
for the definition of Baxter permutations.EXAMPLES:
sage: from sage.combinat.baxter_permutations import BaxterPermutations_size sage: BaxterPermutations_size(5) Baxter permutations of size 5