On the Number of Slopes of the Graph of a Function Defined on a Finite Field
✍ Scribed by A. Blokhuis; S. Ball; A.E. Brouwer; L. Storme; T. Szőnyi
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 116 KB
- Volume
- 86
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
✦ Synopsis
Given a set U of size q in an affine plane of order q, we determine the possibilities for the number of directions of secants of U, and in many cases characterize the sets U with given number of secant directions.
📜 SIMILAR VOLUMES
The interval number of a simple undirected graph G, denoted i(G), is the least nonnegative integer r for which we can assign to each vertex in G a collection of at most r intervals on the real line such that two distinct vertices u and w of G are adjacent if and only if some interval for u intersect
The interval number of a (simple, undirected) graph G is the least positive integer t such that G is the intersection graph of sets, each of which is the union of t real intervals. A chordal (or triangulated) graph is one with no induced cycles on 4 or more vertices. If G is chordal and has maximum
In this paper, we give a reduction theorem for the number of solutions of any diagonal equation over a finite field. Using this reduction theorem and the theory of quadratic equations over a finite field, we also get an explicit formula for the number of solutions of a diagonal equation over a finit
In this paper, some characterizations of median and quasi-median graphs are extended to general isometric subgraphs of Cartesian products using the concept of an imprint function as introduced by Tardif. This extends the well known concepts of medians in median graphs as well as imprints in quasi-me
The number of spanning trees in a finite graph is first expressed as the derivative (at 1) of a determinant and then in terms of a zeta function. This generalizes a result of Hashimoto to non-regular graphs. ## 1998 Academic Press Let G be a finite graph. The complexity of G, denoted }, is the num