𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Exponential number of inequivalent difference sets in ℤ

✍ Scribed by James A. Davis; Deirdre L. Smeltzer

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
140 KB
Volume
11
Category
Article
ISSN
1063-8539

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Kantor [5] proved an exponential lower bound on the number of pairwise inequivalent difference sets in the elementary abelian group of order 2^2s+2^. Dillon [3] generalized a technique of McFarland [6] to provide a framework for determining the number of inequivalent difference sets in 2‐groups with a large elementary abelian direct factor. In this paper, we consider the opposite end of the spectrum, the rank 2 group ℤ
, and compute an exponential lower bound on the number of pairwise inequivalent difference sets in this group. In the process, we demonstrate that Dillon difference sets in groups ℤ
can be constructed via the recursive construction from [2] and we show that there are exponentially many pairwise inequivalent difference sets that are inequivalent to any Dillon difference set. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 249–259, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jcd.10046

📜 SIMILAR VOLUMES

Relative difference sets, graphs and ine
Relative difference sets, graphs and inequivalence of functions between groups
✍ K. J. Horadam 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 154 KB

## Abstract For cryptographic purposes, we want to find functions with both low differential uniformity and dissimilarity to all linear functions and to know when such functions are essentially different. For vectorial Boolean functions, extended affine equivalence and the coarser Carlet–Charpin–Zi

Asymptotic Nonexistence of Difference Se
Asymptotic Nonexistence of Difference Sets in Dihedral Groups
✍ Ka Hin Leung; Bernhard Schmidt 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 190 KB

We prove that for any primes p 1 ; . . . ; p s there are only finitely many numbers Q s i¼1 p ai i ; a i 2 Z þ ; which can be orders of dihedral difference sets. We show that, with the possible exception of n ¼ 540; 225; there is no difference set of order n with 15n410 6 in any dihedral group.

New difference sets in nonabelian groups
New difference sets in nonabelian groups of order 100
✍ Anka Golemac; Tanja Vučičić 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 126 KB

## Abstract In two groups of order 100 new difference sets are constructed. The existence of a difference set in one of them has not been known. The correspondence between a (100, 45, 20) symmetric design having regular automorphism group and a difference set with the same parameters has been used

On the maximum number of different order
On the maximum number of different ordered pairs of symbols in sets of latin squares
✍ Jeffrey H. Dinitz; Douglas R. Stinson 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 140 KB 👁 1 views

## Abstract In this paper, we study the problem of constructing sets of __s__ latin squares of order __m__ such that the average number of different ordered pairs obtained by superimposing two of the __s__ squares in the set is as large as possible. We solve this problem (for all __s__) when __m__

The number of maximal independent sets i
The number of maximal independent sets in connected graphs
✍ Zoltán Füredi 📂 Article 📅 1987 🏛 John Wiley and Sons 🌐 English ⚖ 286 KB 👁 2 views

Generalizing a theorem of Moon and Moser. we determine the maximum number of maximal independent sets in a connected graph on n vertices for n sufficiently large, e.g., n > 50. = I .32. . .). Example 1.2. Let b, = i(C,), where C,z denotes the circuit of length n. Then b, = 3, 6, = 2, b, = 5, and b,

Constraints on the number of maximal ind
Constraints on the number of maximal independent sets in graphs
✍ Jiuqiang Liu 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 387 KB 👁 2 views

## Abstract A maximal independent set of a graph __G__ is an independent set that is not contained properly in any other independent set of __G__. Let __i(G)__ denote the number of maximal independent sets of __G__. Here, we prove two conjectures, suggested by P. Erdös, that the maximum number of m