We determined the inner products of two conformal vectors with central charge 1 2 whose τ -involutions generates S3 if none of τ -involutions are trivial. We also see that a subVA generated by such conformal vectors is a VOA with central charge 1 2 + 20 21 or 4 5 + 6 7 and has a Griess algebra of dimension three or four, respectively.

which has a straightforward combinatorial proof when an is the number of involutions of [n], must also hold when an is the number of Young tableaux on [n]. In this paper, we first give (Section 3) a combinatorial proof of (1) for Young tableaux which agrees under the Robinson-Schensted correspondence with the proof for involutions. The proof involves a recursive construction which depends in pa...

It is well-known that a nonsingular minimal cubic surface is birationally rigid; the group of its birational selfmaps is generated by biregular selfmaps and birational involutions such that all relations between the latter are implied by standard relations between reflections on an elliptic curve. It is also known that a factorial nodal quartic threefold is birationally rigid and its group of b...

Baxter numbers are known to count several families of combinatorial objects, all of which come equipped with natural involutions. In this paper, we add a combinatorial family to the list, and show that the known bijections between these objects respect these involutions. We also give a formula for the number of objects fixed under this involution, showing that it is an instance of Stembridge’s ...

We study the generating function for the number of involutions on n letters containing exactly r 0 occurrences of 231. It is shown that finding this function for a given r amounts to a routine check of all involutions of length at most 2r + 2. © 2006 Elsevier B.V. All rights reserved.

An S3-involution graph for a group G is a graph with vertex set a union of conjugacy classes of involutions of G such that two involutions are adjacent if they generate an S3-subgroup in a particular set of conjugacy classes. We investigate such graphs in general and also for the case where G = PSL(2, q).

An S3-involution graph for a group G is a graph with vertex set a union of conjugacy classes of involutions of G such that two involutions are adjacent if they generate an S3-subgroup in a particular set of conjugacy classes. We investigate such graphs in general and also for the case where G = PSL(2, q). 2000 Mathematics subject classification: 20B25, 05C25.

We study the generating function for the number of involutions on n letters containing exactly r ≥ 0 occurrences of 3412. It is shown that finding this function for a given r amounts to a routine check of all involutions on 2r + 1 letters. 2000 Mathematics Subject Classification: Primary 05A05, 05A15; Secondary 05C90

A fixed-point free involution on a finite set S is defined as a bijection I : S → S such as ∀e ∈ S, I(I(e)) = e and ∀e ∈ S, I(e) 6= e. In this article, the fixed-point free involutions are represented as partitions of the set S, and some properties linked to this representation are exhibited. Then an optimal algorithm to list all the fixed-point free involutions is presented. Its soundess relie...

Several authors have examined connections among restricted permutations, continued fractions, and Chebyshev polynomials of the second kind. In this paper we prove analogues of these results for involutions which avoid 3412. Our results include a recursive procedure for computing the generating function for involutions which avoid 3412 and any set of additional patterns. We use our results to gi...