A198434 Number of simple symmetric permutations of degree 2n (or 2n+1).

2, 10, 90, 966, 12338, 181470, 3018082, 55995486, 1146939010, 25716746430, 626755197698, 16502357651966, 466944932413442, 14133259249586174, 455715081098876418, 15596665064842012158, 564724372634695925762, 21568978799171323200510, 866674159679235417061378, 36548294282449538711357438

Offset

2,1

Comments

A permutation is simple if the only intervals that are fixed are the singletons and [1..m].

A permutation p is symmetric if i+j=m+1 implies p(i)+p(j)=m+1.

For example the permutations

1234 and 12345

2413 25314

are both simple and symmetric.

Symmetric simple permutations of degree 2n+1 correspond to simple permutations in the Weyl group of type B_n.

Symmetric simple permutations of degree 2n correspond to simple permutations in the Weyl group of type C_n.

These occur in pairs so all entries in this sequence will be even.

Links

Table of n, a(n) for n=2..21.

R. Dewji, I. Dimitrov, A. McCabe, M. Roth, D. Wehlau and J. Wilson,

Decomposing Inversion Sets of Permutations and Applications to Faces of the Littlewood-Richardson Cone, arXiv:1110.5880v1[math.CO]

Example

The simple symmetric permutations of lowest degree are 2413, 3142, 25314, 41325.

Crossrefs

Cf. A111111.

Sequence in context: A363425 A338050 A366268 * A326089 A277403 A179423

Adjacent sequences: A198431 A198432 A198433 * A198435 A198436 A198437

Keyword

nonn

Author

David Wehlau, Oct 24 2011

Status

approved