We present a group theoretic construction of the Virasoro algebra in the framework of wreath products. This can be regarded as a counterpart of a geometric construction of Lehn in the theory of Hilbert schemes of points on a surface. Introduction It is by now well known that a direct sum ⊕ n≥0R(Sn) of the Grothendieck rings of symmetric groups Sn can be identified with the Fock space of the Hei...

This paper studies the cycle indices of products of permutation groups. The main focus is on the product action of the direct product of permutation groups. The number of orbits of the product on n-tuples is trivial to compute from the numbers of orbits of the factors; on the other hand, computing the cycle index of the product is more intricate. Reconciling the two computations leads to some i...

We examine languages of unranked forests definable using the temporal operators EF and EX. We characterize the languages definable in this logic, and various fragments thereof, using the syntactic forest algebras introduced by Bojanczyk and Walukiewicz. Our algebraic characterizations yield efficient algorithms for deciding when a given language of forests is definable in this logic. The proofs...

Let G be a group acting faithfully on a set X . The distinguishing number of the action of G on X , denoted DG(X ), is the smallest number of colors such that there exists a coloring of X where no nontrivial group element induces a colorpreserving permutation of X . In this paper, we consider the distinguishing number of two important product actions, the wreath product and the direct product. ...

In this paper, we study the subconstituent algebras, also called as Terwilliger algebras, of association schemes that are obtained as the wreath product of one-class association schemes Kn = H(1, n) for n ≥ 2. We find that the d-class association scheme Kn1 o Kn2 o · · · o Knd formed by taking the wreath product of Kni has the triple-regularity property. We determine the dimension of the Terwil...

In this paper, we study the wreath product of one-class association schemes Kn =H(1, n) for n≥ 2. We show that the d-class association scheme Kn1 Kn2 · · · Knd formed by taking the wreath product of Kni (for ni ≥ 2) has the triple-regularity property. Then based on this fact, we determine the structure of the Terwilliger algebra of Kn1 Kn2 · · · Knd by studying its irreducible modules. In parti...