We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
To save content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about saving content to .
To save content items to your Kindle, first ensure no-reply@cambridge.org
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
The structure is determined for the existence of some amicable weighing matrices. This is then used to prove the existence and non-existence of some amicable orthogonal designs in powers of two.
An equidistant permutation array (EPA) is a ν × r array defined on an r-set, R, such that (i) each row is a permutation of the elements of R and (ii) any two distinct rows agree in λ positions (that is, the Hamming distance is (r−λ)).
Such an array is said to have order ν. In this paper we give several recursive constructions for EPA's.
The first construction uses a resolvable regular pairwise balanced design of order v to construct an EPA of order ν. The second construction is a generalization of the direct product construction for Room squares.
We also give a construction for intersection permutation arrays, which arrays are a generalization of EPA's.
The purpose of this paper is to demonstrate that a number of properties of independence spaces are of finite character, thus making it possible to easily generalise known theorems for finite spaces, or matroids, to independence spaces on infinite sets.