This paper is concerned with certain point-sets T in a projective plane PG (2, q) over GF (q) which have only three characters with respect to the lines. We assume throughout this paper that for any line l of π
where
It is easily seen that if t = 1 then T is a (q + 1)-arc, i.e. an oval; otherwise T is a (q+t, t)-arc of type (0, 2, t). Therefore (q+t, t)-arcs of type (0, 2, t) appear to be a generalization of ovals and there are interesting connections between ovals and (q + t, t)-arcs of type (0, 2, t) from various points of view. Our purpose is to investigate such particular (k, t)-arcs using some ideas of B. Segre developed for ovals in three fundamental papers [16, 17, 18]. For these papers and more recent results in this direction the reader is referred to [6], chapter 10 and [9]. General results concerning (k, n)-arcs may be found in [6], chapter 12; see also [4, 7, 20, 23].