Combinatorially fruitful properties of 3⋅2−1 and 3⋅2−2 modulo p

Anderson, I. and Preece, D.A. (2010) Combinatorially fruitful properties of 3⋅2−1 and 3⋅2−2 modulo p. Discrete Mathematics, 310(2), pp. 312-324. (doi: 10.1016/j.disc.2008.09.046)

Abstract

Write a equivalent to 3 . 2(-1) and b equivalent to 3 . 2(-2) (mod p) where p is an odd prime. Let c be a value that is congruent (mod p) to either a or b. For any x from Z(p)\{0}, evaluate each of x and cx (mod p) within the interval (0, p). Then consider the quantity mu(c)*(x) = min(cx - x, x - cx) where the differences are evaluated (mod p - 1, not mod p) in the interval (0, p - 1), and the quantity mu(boolean AND)(c)(x) = min(cx - x, x - cx) where the differences are evaluated (mod p + 1) in the interval (0, p + 1). As x varies over Zp\{0}, the values of each of mu(c)*(x) and mu(boolean AND)(c)(x) give exactly two occurrences of nearly every member of 1, 2, (p, - 1)/2. This fact enables a and b to be used in constructing some terraces for Z(p-1) andZ(p+l) from segments of elements that are themselves initially evaluated in Z(p).

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Anderson, Dr Ian
• Authors: Anderson, I., and Preece, D.A.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Discrete Mathematics
• ISSN: 0012-365X