A129776 Number of maximally-clustered hexagon-avoiding permutations in S_n; the maximally-clustered hexagon-avoiding permutations are those that avoid 3421, 4312, 4321, 46718235, 46781235, 56718234, 56781234.

1, 1, 2, 6, 21, 78, 298, 1157, 4535, 17872, 70644, 279704, 1108462, 4395045, 17431206, 69144643, 274300461, 1088215370, 4317321235, 17128527716, 67956202025, 269612504850, 1069675361622, 4243893926396, 16837490364983, 66802139457897, 265035151393777

Offset: 0

Author

Brant Jones (brant(AT)math.washington.edu), May 17 2007

Keywords

• nonn

Comments

If w is maximally-clustered and hexagon-avoiding, there are simple explicit formulas for all the Kazhdan-Lusztig polynomials P_{x,w}.

Examples

			a(8)=4535 because there are 4535 permutations of size 8 that avoid 3421, 4312, 4321, 46718235, 46781235, 56718234 and 56781234.
		

References

• Jozsef Losonczy, Maximally clustered elements and Schubert varieties, Ann. Comb. 11 (2007), no. 2, 195-212.

Links

• H. Denoncourt and B. Jones, The enumeration of maximally clustered permutations.
• B. Jones, Kazhdan--Lusztig polynomials for maximally-clustered hexagon-avoiding permutations.

Crossrefs

Cf. A058094, A108600.

Programs

PARI

lista(nt) = { my(x = 'x + 'x*O('x^nt) ); P = (3*x^6+x^5-5*x^4+7*x^3-5*x^2+x) / (-3*x^6+4*x^5+8*x^4-14*x^3+15*x^2-7*x+1); print(Vec(P));} \\ Michel Marcus, Mar 17 2013

Formula

G.f.: 1+(3x^6+x^5-5x^4+7x^3-5x^2+x) / (-3x^6+4x^5+8x^4-14x^3+15x^2-7x+1).

Extensions

More terms from Michel Marcus, Mar 17 2013

a(0)=1 prepended by Alois P. Heinz, Jan 12 2025