ar X iv : 0 80 8 . 36 76 v 3 [ m at h . C O ] 3 1 Ju l 2 00 9 Pseudocyclic Association Schemes and Strongly Regular Graphs

ar X iv : 0 70 9 . 05 64 v 1 [ m at h . C O ] 5 S ep 2 00 7 3 - bounded Property in a Triangle - free Distance - regular Graph ∗

Let Γ denote a distance-regular graph with classical parameters (D, b, α, β) and D ≥ 3. Assume the intersection numbers a1 = 0 and a2 6= 0. We show Γ is 3-bounded in the sense of the article [D-bounded distance-regular graphs, European Journal of Combinatorics(1997)18, 211-229].

1 6 A pr 2 00 9 Pseudocyclic Association Schemes and Strongly Regular Graphs

Let X be a pseudocyclic association scheme in which all the nontrivial relations are strongly regular graphs with the same eigenvalues. We prove that the principal part of the first eigenmatrix of X is a linear combination of an incidence matrix of a symmetric design and the all-ones matrix. Amorphous pseudocyclic association schemes are examples of such association schemes whose associated sym...

ar X iv : 0 70 7 . 33 03 v 1 [ m at h . O A ] 2 3 Ju l 2 00 7 OPERATOR - VALUED FRAMES

ar X iv : 0 80 7 . 35 76 v 1 [ m at h . A G ] 2 3 Ju l 2 00 8 LINEAR RELATIONS BETWEEN POLYNOMIAL ORBITS

We study the orbits of a polynomial f ∈ C[X], namely the sets {α, f(α), f(f(α)), . . . } with α ∈ C. We prove that if two nonlinear complex polynomials f, g have orbits with infinite intersection, then f and g have a common iterate. More generally, we describe the intersection of any line in C with a d-tuple of orbits of nonlinear polynomials, and we formulate a question which generalizes both ...

ar X iv : 0 80 7 . 00 58 v 2 [ m at h . D G ] 1 6 Ju l 2 00 8 EQUIVARIANT DIFFERENTIAL CHARACTERS AND SYMPLECTIC REDUCTION

We describe equivariant differential characters (classifying equi-variant circle bundles with connections), their prequantization, and reduction.