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We give some very interesting matrices which are orthogonal over groups and, as far as we know, referenced, but in fact undocumented. This note is not intended to be published but available for archival reasons.
Comment: 15 pages
Comment: 15 pages
Externí odkaz:
http://arxiv.org/abs/1510.06816
Motivated by a question in origami, we consider sets of points in the complex plane constructed in the following way. Let $L_\alpha(p)$ be the line in the complex plane through $p$ with angle $\alpha$ (with respect to the real axis). Given a fixed co
Externí odkaz:
http://arxiv.org/abs/1011.2769
Autor:
de Launey, Warwick, Gordon, Daniel M.
Let $S(x)$ be the number of $n \leq x$ for which a Hadamard matrix of order $n$ exists. Hadamard's conjecture states that $S(x)$ is about $x/4$. From Paley's constructions of Hadamard matrices, we have that \[ S(x) = \Omega(x/\log x). \] In a recent
Externí odkaz:
http://arxiv.org/abs/1004.4872
Autor:
de Launey, Warwick, Levin, David A.
In this paper, we study a family of lattice walks which are related to the Hadamard conjecture. There is a bijection between paths of these walks which originate and terminate at the origin and equivalence classes of partial Hadamard matrices. Theref
Externí odkaz:
http://arxiv.org/abs/1003.4003
Autor:
de Launey, Warwick
Publikováno v:
Journal of Combinatorial Theory, Series A 116 (2009) 1002-1008.
It is conjectured that Hadamard matrices exist for all orders $4t$ ($t>0$). However, despite a sustained effort over more than five decades, the strongest overall existence results are asymptotic results of the form: for all odd natural numbers $k$,
Externí odkaz:
http://arxiv.org/abs/1003.4001
Autor:
de Launey, Warwick, Kharaghani, H.
Publikováno v:
In Journal of Combinatorial Theory, Series A 2009 116(6):1140-1153
Publikováno v:
In Discrete Mathematics 2008 308(13):2910-2924
Autor:
Khodkar, Abdollah, de Launey, Warwick
Publikováno v:
In Discrete Mathematics 2008 308(13):2896-2900
Autor:
Craigen, Robert1 craigenr@cc.umanitoba.ca, de Launey, Warwick2
Publikováno v:
Journal of Combinatorial Designs. Sep2016, Vol. 24 Issue 9, p406-420. 15p.