OFFSET
0,2
COMMENTS
a(n) is also the number of decorated permutations whose chordal diagram is a separable union of star graphs.
a(n) is also the number of decorated permutations whose chordal diagram contains no crossed alignments.
LINKS
Jordan Weaver, Table of n, a(n) for n = 0..50
Sara C. Billey and Jordan E. Weaver, Criteria for smoothness of Positroid varieties via pattern avoidance, Johnson graphs, and spirographs, arXiv:2207.06508 [math.CO], 2022.
S. Corteel, Crossings and alignments of permutations, arXiv:math/0601469 [math.CO], 2006.
A. Knutson, T. Lam and D. Speyer, Positroid varieties: juggling and geometry, Compos. Math. 149 (2013), no. 10, 1710-1752.
A. Postnikov, Total positivity, Grassmannians, and networks, arXiv:math/0609764 [math.CO], 2006.
FORMULA
EXAMPLE
For n = 3, the a(3) = 16 positroids correspond the decorated permutations with underlying permutations 231, 312, 321, 213, 132, and 123 in one-line notation. Each fixed point, e.g., the 2 in 321, can be colored in two ways. Hence 321, 213, and 132 contribute 2 decorated permutations each, 123 contributes 8, while 231 and 312 each contribute 1.
CROSSREFS
KEYWORD
nonn
AUTHOR
Jordan Weaver, Nov 17 2021
EXTENSIONS
a(10)-a(23) from Jordan Weaver, Apr 19 2022
STATUS
approved
