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A295704 Number of equivalence classes of 132-avoiding permutations of [n], where two permutations are equivalent if they have the same set of pure descents. 0
1, 1, 2, 4, 10, 26, 66, 169, 437, 1130, 2926, 7597, 19749, 51381, 133812, 348755, 909464, 2372862, 6193720 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

As defined in Baril et al., a pure descent of a permutation p is a pair of the form (p_i, p_(i+1)) such that p_i > p_(i+1) and there is no j < i such that p_i > p_j > p_(i+1).

LINKS

Table of n, a(n) for n=0..18.

Jean-Luc Baril, Sergey Kirgizov, Armen Petrossian, Forests and pattern-avoiding permutations modulo pure descents, Permutation Patterns 2017, Reykjavik University, Iceland, June 26-30, 2017. See Section 5.

PROG

(Sage)

def DD(p) :

pure_descents = []

occur = 0

for i in range(len(p)-1) :

hi = p[i]; lo = p[i+1]

mask = ((1 << (hi - lo)) - 1) << lo

if hi > lo and not (occur & mask) :

pure_descents.append((hi, lo))

occur |= 1 << hi

pure_descents.sort()

return pure_descents

def a(n): return len({tuple(DD(p)) for p in Permutations(n, avoiding=[1, 3, 2])})

CROSSREFS

Cf. A005773 (analogous sequence for 123-avoiding permutations), A152225 (conjecturally analogous sequence for 213-avoiding permutations).

Sequence in context: A055775 A239076 A217988 * A090032 A090377 A151278

Adjacent sequences: A295701 A295702 A295703 * A295705 A295706 A295707

KEYWORD

nonn,more

AUTHOR

Eric M. Schmidt, Nov 25 2017

STATUS

approved

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Last modified January 31 05:36 EST 2023. Contains 359947 sequences. (Running on oeis4.)