An infinite family of vertex-and edge-transitive, but not arc-transitive, graphs of degree 4 is constructed.

We provide character-free proofs of some results on idempotents in p-adic group rings, centering around Brauer's Second Main Theorem on Blocks.

Let fn be a sequence of nonnegative integers and let f(x): = Σn≥0 fn xn be its generating function. Assume f(x) has the following properties: it has radius of convergence r, 0 < r < 1, with its only singualarity on the circle of convergence at x = r and f(r) = s; y = f(x) satisfies an analytic identity F(x, y) = 0 near (r, s); for some k ≥ 2 F0.j = 0, 0 ≤ j < k, F0.k ≠ 0 where Fi is the value at (r, s) of the ith partial derivative with respect to x and the jth partial derivative with respect to y of F. These assumptions form the basis of what we call the typical and general cases. In both cases we show how to obtain an asymptotic expansion of fn. We apply our technique to produce several terms in the asymptotic expansion of combinatorial sequences for which previously only the first term was known.

Using Fourier transforms, we give a new proof of certain identites for the fundamental solutions of the iterated Dirac operators and Ḏl = (Σ/Σx0 + Ḏ)l. Based on the close relationship between the fundamental solutions and the conformal weights we then give a simple proof of B. Bojarski's results on the conformal covariance of Ḏl. We also prove a new conformal covatiance result of D.

If h is the composition of two formal power series f and g, and if h is even, what can be said about f and g? Some partial answers are given here.

In [1], the notion of a local join (meet) endomorphism of a lattice was defied. This notion, though interesting in the context of infinitary lattice operations, is redundant in the finitary setting, so its removal from all hypotheses does not affect the results presented therein. The author regrets this oversight and wishes to thank those readers who are patient enough to read over this error.