𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Extended Langford Sequences with Small Defects

✍ Scribed by Václav Linek; Zhike Jiang

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
284 KB
Volume
84
Category
Article
ISSN
0097-3165

No coin nor oath required. For personal study only.

✦ Synopsis

A k-extended Langford sequence of defect d and length m is a sequence s 1 , s 2 , ..., s 2m+1 in which s k ==, where = is the null symbol, and each other member of the sequence comes from the set [d, d+1, ..., d+m&1]. Each j # [d, d+1, ..., d+m&1] occurs exactly twice in the sequence, and the two occurrences are separated by exactly j&1 symbols. In this paper we prove that when d=2, 3, the necessary conditions for the existence of such a sequence are sufficient. 1998 Academic Press Theorem 1.1 [3]. A Langford sequence of defect d and length m exists if and only if (1) m 2d&1 and

(2) m#0, 1 (mod 4) for d odd and m#0, 3 (mod 4) for d even.

📜 SIMILAR VOLUMES

Langford sequences: Some connections wit
Langford sequences: Some connections with complete and additive permutations
✍ Sadao Saito; Takanori Hayasaka 📂 Article 📅 1990 🏛 Elsevier Science 🌐 English ⚖ 444 KB

We explore the relations between Langford (2, m, 3m)-sequences on the one hand and complete and addtive permutations on the other. We consider in this context permutations with a certain "splitting" property and report on the results of some computer studies.

On partitions of {1,…,2m + 1}{k} into di
On partitions of {1,…,2m + 1}{k} into differences d,…,d + m − 1: Extended Langford sequences of large defect
✍ Vaclav Linek; Shai Mor 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 170 KB

## Abstract It is shown that for __m__ = 2__d__ − 1, 2__d__, 2__d__ + 1, and __d__ ≥ 1, the set {1, 2,…, 2__m__ + 2}, − {2,__k__} can be partitioned into differences __d__,__d__ + 1,…,__d__ + __m__ − 1 whenever (__m__,__k__) ≡ (0,0), (1,__d__ + 1), (2, 1), (3,__d__) (mod (4,2)) and (__d__,__m__,__k

Two-step sequences with extended temkin
Two-step sequences with extended temkin nonuniform reactivity—Rate-determining step revisited
✍ Vlad T. Popa; James A. Schwarz 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 581 KB

Within the Temkin-type approach for two-step mechanisms, the problem of the rate-determining step (rds) and its possible shift on a nonuniform surface is reexamined. The nonuniformity concept is extended to its maximum limits and a new transfer rule is derived for the model's intrinsic linear free e

Multicontrast sequences with continuous
Multicontrast sequences with continuous table motion: A novel acquisition technique for extended field of view imaging
✍ Gregor Sommer; Hans-Peter Fautz; Ute Ludwig; Jürgen Hennig 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 368 KB

## Abstract A novel acquisition technique called multicontrast imaging is presented that provides multiple datasets of different image contrasts covering an extended field of view within one measurement procedure. The technique uses a continuously moving table and is based on the repetitive acquisi