B2-sequences and the distinct distance constant

✍ Scribed by G.S Yovanof; H Taylor

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 392 KB
• Volume: 39
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/s0898-1221(00)00105-x

✦ Synopsis

ferences c U -ai, i < j are distinct is called a B2-sequence. Denote by DDC (distinct difference constant) the maximum over all possible B2-sequences of the sum E(1/ai). Previously known upper and lower bounds for the DDC are 2.1597 < DDC < 2.374. We have estimated the following sharper bounds on DDC: 2.1600383 < DDC < 2.2473. We have further proved that any B2-sequence which achieves the maximum reciprocal sum must start with the terms 1,2,4. (~) 2000 Elsevier Science Ltd. All rights reserved.