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Cocyclic Orthogonal Designs and the Asymptotic Existence of Cocyclic Hadamard Matrices and Maximal Size Relative Difference Sets with Forbidden Subgroup of Size 2

2001
*
Journal of combinatorial theory. Series A
*

Then there is a normal

doi:10.1006/jcta.2000.3062
fatcat:hycctamiobfmxnozq2s5jgowte
*relative**difference**set**of**size**2*t s*with**forbidden**subgroup*(z) in*the*group T_S." ... This paper contains a discussion*of**cocyclic**Hadamard**matrices*, their associated*relative**difference**sets*,*and*regular group actions. ... We use*the*notation NRDS(v, k, *, m) to denote a normal*relative**difference**set**of**size*k in a group*of**size*v*with**forbidden**subgroup**of**size*m*and*index *. ...##
###
Page 47 of Mathematical Reviews Vol. , Issue 2002A
[page]

2002
*
Mathematical Reviews
*

*Cocyclic*

*orthogonal*

*designs*

*and*

*the*

*asymptotic*

*existence*

*of*

*cocyclic*

*Hadamard*

*matrices*

*and*

*maximal*

*size*

*relative*

*difference*

*sets*

*with*

*forbidden*

*subgroup*

*of*

*size*

*2*. (English summary) J. Combin. ...

*The*authors note that Dg does not contain any

*relative*(4, 2,4,

*2*)-

*difference*

*set*

*relative*to a normal

*subgroup*

*of*order

*2*, though it does contain such an RDS

*relative*to a nonnormal one

*The*proof uses ...

##
###
Page 873 of Mathematical Reviews Vol. , Issue 2001B
[page]

2001
*
Mathematical Reviews
*

Smith, “

*Cocyclic**orthogonal**designs**and**the**asymptotic**existence**of**maximal**size**relative**difference**sets**with**forbidden**subgroup**size**2*”, Preprint, 1998; per bibl.]). ... However, there*exist**relative*(4,*2*, 41, 2t)-*difference**sets**relative*to nonnormal*subgroups**of*order*2*, in groups which have no central RDS*with*these parameters (for example Dg [W. de Launey*and*M. ...##
###
On the asymptotic existence of cocyclic Hadamard matrices

2009
*
Journal of combinatorial theory. Series A
*

We also show that if

doi:10.1016/j.jcta.2009.03.002
fatcat:5cgvx6vbgvfvfbq4kwwsd3u5ei
*the*binary expansion*of*q contains N ones, then there is a*cocyclic**Hadamard*matrix*of*order*2*4N−*2*q. ... We prove there is a*cocyclic**Hadamard*matrix*of*order*2*10+t q whenever t 8 log*2*(q−1) 10 . ... Acknowledgments*The*authors thank*the*referees for their valuable help in*the*preparation*of*this article. ...##
###
Page 137 of Mathematical Reviews Vol. , Issue Subject Index
[page]

*
Mathematical Reviews
*

*Cocyclic*

*orthogonal*

*designs*

*and*

*the*

*asymptotic*

*existence*

*of*

*cocyclic*

*Hadamard*

*matrices*

*and*

*maximal*

*size*

*relative*

*difference*

*sets*

*with*

*forbidden*

*subgroup*

*of*

*size*

*2*. ...

*Cocyclic*

*orthogonal*

*designs*

*and*

*the*

*asymptotic*

*existence*

*of*

*cocyclic*

*Hadamard*

*matrices*

*and*

*maximal*

*size*

*relative*

*difference*

*sets*

*with*

*forbidden*

*subgroup*

*of*

*size*

*2*. ...

##
###
Invitation to Hadamard matrices
[article]

2022
*
arXiv
*
pre-print

*The*main example is

*the*Fourier matrix, F_N=(w^ij)

*with*w=e^

*2*π i/N. We discuss here

*the*basic theory

*of*such

*matrices*,

*with*emphasis on geometric

*and*analytic aspects. ... A complex

*Hadamard*matrix is a square matrix H∈ M_N(ℂ) whose entries are on

*the*unit circle, |H_ij|=1,

*and*whose rows

*and*pairwise

*orthogonal*. ... As a conclusion to this study, looking at

*the*

*maximizers*H ∈ M N (±1)

*of*

*the*quantity | det H| is not exactly an ideal method, when looking for analogues

*of*

*the*

*Hadamard*

*matrices*at

*the*

*forbidden*

*size*...

##
###
Page 1088 of Mathematical Reviews Vol. , Issue Author Index
[page]

*
Mathematical Reviews
*

*Cocyclic*

*orthogonal*

*designs*

*and*

*the*

*asymptotic*

*existence*

*of*

*cocyclic*

*Hadamard*

*matrices*

*and*

*maximal*

*size*

*relative*

*difference*

*sets*

*with*

*forbidden*

*subgroup*

*of*

*size*

*2*. (English summary) J. Combin. ... (Summary) 2002m:05036 05B05 — (

*with*Magliveras, Spyros S.; Wassermann, Alfred) New large

*sets*

*of*t-

*designs*. (English summary) J. Combin. Des. 9 (2001), no. 1, 40-59. ...

##
###
Page 1857 of Mathematical Reviews Vol. , Issue Author Index
[page]

*
Mathematical Reviews
*

(

*with*de Launey, Warwick)*Cocyclic**orthogonal**designs**and**the**asymptotic**existence**of**cocyclic**Hadamard**matrices**and**maximal**size**relative**difference**sets**with**forbidden**subgroup**of**size**2*. ... (*with*Adem, Alejandro) Periodic complexes*and*group actions. (English summary) Ann.*of*Math. (*2*) 154 (2001), no.*2*, 407-435. ...##
###
Transformation & Uncertainty. Some Thoughts on Quantum Probability Theory, Quantum Statistics, and Natural Bundles
[article]

2010
*
arXiv
*
pre-print

*of*decoherence

*and*

*the*impossibility

*of*perfect joint measurement. ... We then propose a two-step strategy to determine

*the*(possibly mixed) state

*of*n identically prepared qubits,

*and*prove that it is

*asymptotically*optimal in a local minimax sense, using 'Quantum Local ... Two Lemmas We

*set*out to prove theorem 7.23. We start

*with*two lemmas

*designed*to explicate

*the*homomorphism ρ : G(k, M ) → GL(R n ) × Z G. ...

##
###
Lyapunov Exponents in the Spectral Theory of Primitive Inflation Systems

2019

In this work, we consider primitive inflation rules as generators

doi:10.4119/unibi/2935972
fatcat:nfzju7dagzemdn3pkrra3frcji
*of*aperiodic tilings,*and*subsequently,*of*aperiodic point*sets*(which are toy models for quasicrystals) deemed adequate for diffraction ... We show that this holds for large classes*of*systems,*and*, as a sanity check, show that*the*necessary criterion for*existence*is satisfied by systems which are a priori known to have absolutely continuous ... Instead, we take advantage*of**the*five-fold symmetry*of*a GLB tiling*and*work*with*a*different**set**of*generators. ...##
###
Toward a Generalized Shapiro and Shapiro Conjecture
[chapter]

2011
*
PROGRESS IN MATHEMATICS
*

Use in connection

doi:10.1007/978-0-8176-8277-4_4
fatcat:jh7utclvbve43ja7pghc6bp3fi
*with*any form*of*information storage*and*retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is*forbidden*. ... On*the*Content*of*This Volume xvii*the*fact that rational unknots in tight contact structures on lens spaces are weakly transversely simple*and*Legendrian simple. ... He extends his special thanks to Ilia Itenberg, Burglind Jöricke,*and*Mikael Passare,*the*editors*of*these proceedings, for their patience*with**the*author. ...##
###
A Mathematical Bibliography of Signed and Gain Graphs and Allied Areas Compiled by

1996
unpublished

Generalizations

fatcat:os5lveptfbbbplmcy4drb2zd3m
*of*§ §3, 4 are sketched*and*are applied to find*the*number*of*H-equivalent*matrices**of*given*size**with*entries ±1, ±1, . . . , ±k. ... There*exist*pairs*of*unbalanced, strictly quasicospectral graphs;*existence**of*larger*sets*is unsolved. ...*The*property is*the**existence**of*an Eulerian cut.*The**asymptotic*probability is .57 . . .. [Problem. Generalize to gain graphs*with*finite gain group, esp. to signed graphs. ...