A224240 - OEIS

A224240

Number of rationally smooth Schubert varieties of type B_n (also type C_n).

1, 2, 8, 34, 142, 596, 2530, 10842, 46766, 202594, 880210, 3832004, 16707034, 72919268, 318523238, 1392241660, 6088401738, 26635608428, 116562456250, 510229227402, 2233891550606, 9782115379270, 42841485831558, 187649299437218, 821999681312518

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OFFSET

0,2

COMMENTS

Also, the number of signed permutations w in the hyperoctahedral group whose initial interval [id,w] in Bruhat order is rank symmetric. Equivalently, the Kazhdan-Lusztig polynomial P_id,w(q) = 1. Characterized by pattern avoidance.

LINKS

Table of n, a(n) for n=0..24.

Sara C. Billey, Pattern Avoidance and Rational Smoothness of Schubert varieties, Advances in Math, vol. 139 (1998) pp. 141-156.

Edward Richmond and William Slofstra, Staircase diagrams and enumeration of smooth Schubert varieties, arXiv:1510.06060 [math.CO], 2015; J. Combin. Theory Ser. A, Vol 150 (2017) pp. 328-376.

FORMULA

From Joel B. Lewis, May 11 2026: (Start)

G.f.: ((1-8*x+23*x^2-29*x^3+14*x^4)+(2*x-6*x^2+7*x^3-2*x^4)*sqrt(1-4*x))/((1-x)^2 * (1-6*x+8*x^2-4*x^3)) (from Richmond--Slofstra).

a(n) = A061539(n) + A224066(n) - A032351(n + 1) (Richmond--Slofstra, remark 9.11). (End)

CROSSREFS

Cf. A032351, A061539, A224066.

Sequence in context: A369836 A228655 A192402 * A014445 A113440 A296227

Adjacent sequences: A224237 A224238 A224239 * A224241 A224242 A224243

KEYWORD

nonn,easy,changed

AUTHOR

Sara Billey, Apr 01 2013

EXTENSIONS

Name edited by and more terms from Joel B. Lewis, May 11 2026

STATUS

approved