๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

The number of self-complementary achiral necklaces

โœ Scribed by E. M. Palmer; A. J. Schwenk

Publisher
John Wiley and Sons
Year
1977
Tongue
English
Weight
304 KB
Volume
1
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

โœฆ Synopsis

Abstract

Necklaces with beads of two colors which are left unchanged both by a reflection as well as by the interchange of the two colors are characterized in terms of their axes of symmetry. This characterization is then used to enumerate them. For n = 2^r^m with r โ‰ฅ 1 and m odd, the number of selfโ€complementary achiral necklaces is magnified image for large even n, this sum is asymptotic to 2^{n/4}โ€1^.

๐Ÿ“œ SIMILAR VOLUMES

A class of self-complementary graphs and
A class of self-complementary graphs and lower bounds of some ramsey numbers
โœ C. R. J. Clapham ๐Ÿ“‚ Article ๐Ÿ“… 1979 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 119 KB ๐Ÿ‘ 1 views

## Abstract A method is described of constructing a class of selfโ€complementary graphs, that includes a selfโ€complementary graph, containing no __K__~5~, with 41 vertices and a selfโ€complementary graph, containing no __K__~7~, with 113 vertices. The latter construction gives the improved Ramsey num

Orientations of Self-complementary Graph
Orientations of Self-complementary Graphs and the Relation of Sperner and Shannon Capacities
โœ A. Sali; G. Simonyi ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 81 KB

We prove that the edges of a self-complementary graph and its complement can be oriented in such a way that they remain isomorphic as digraphs and their union is a transitive tournament. This result is used to explore the relation between the Shannon and Sperner capacity of certain graphs. In partic

Characterization of a planar self-comple
Characterization of a planar self-complementary square-spiral antenna in the THz region
โœ E. R. Brown; A. W. M. Lee; B. S. Navi; J. E. Bjarnason ๐Ÿ“‚ Article ๐Ÿ“… 2006 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 280 KB

This paper describes a compact, self-complementary square-spiral antenna on a GaAs substrate with a broadside high-directivity (ฯณ29 dB) frequency-independent pattern when coupled through a silicon hyperhemisphere. The driving-point resistance undulates between ฯณ100 and 300โ€ from 200 GHz to 1 THz-muc