Publication:
The full metamorphosis of λ-fold block designs with block size four into λ-fold triple systems

Placeholder

Departments

School / College / Institute

Program

KU Authors

Co-Authors

Lindner, Curt

Publication Date

Language

Embargo Status

Journal Title

Journal ISSN

Volume Title

Alternative Title

Abstract

Let (X, B) be a lambda-fold block design with block size 4. If a star is removed from each block of B the resulting collection of triangles T is a partial lambda-fold triple system (X, T). If the edges belonging to the deleted stars can be arranged into a collection of triangles S*, then (X, T boolean OR S*) is a lambda-fold triple system, called a metamorphosis of the lambda-fold block design (X, B) into a lambda-fold triple system. Label the elements of each block b with b(1), b(2), b(3), and b(4) (in any manner). For each i = 1, 2, 3, 4 define a set of triangles T-i and a set of stars S-i as follows: for each block b = [b(1), b(2), b(3), b(4)] belonging to B, partition b into a triangle and a star centered at b(i), and place the triangle in T-i and the star in S-i. Then (X, T-i) is a partial lambda-fold triple system. Now if the edges belonging to the stars in S-i can be arranged into a collection of triangles S-i*, then (X, T-i boolean OR S-i*) is a lambda-fold triple system and we say that M-i = (X, T-i boolean OR S-i*) is the ith metamorphosis of (X, B). The full metamorphosis of (X, B) is the set of four metamorphoses {M-1, M-2, M-3, M-4}. The purpose of this work is to give a complete solution of the following problem: For which n and lambda does there exist a lambda-fold block design with block size 4 having a full metamorphosis into lambda-fold triple systems?

Source

Publisher

Charles Babbage Res Ctr

Subject

Mathematics

Citation

Has Part

Source

Ars Combinatoria

Book Series Title

Edition

DOI

item.page.datauri

Link

Rights

Copyrights Note

Endorsement

Review

Supplemented By

Referenced By

0

Views

0

Downloads