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Unifying some known infinite families of combinatorial 3-designs

2011
*
Journal of combinatorial theory. Series A
*

Those resolvable

doi:10.1016/j.jcta.2010.10.007
fatcat:x6met46akrdo3drftaic3nxmne
*designs*can again be used to obtain*more**infinite*families of simple 3-*designs*through the basic construction. ... Moreover many*infinite*families of simple resolvable 3-*designs*are presented in comparison*with*some known families. ... (iv) As far as the authors know, the family of Theorem 5.4(i) is the first and only known*infinite*family of resolvable Steiner t-*designs**with*t 3 and*block*size bigger*than*4. ...##
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Page 4620 of Mathematical Reviews Vol. , Issue 2000g
[page]

2000
*
Mathematical Reviews
*

k = 4.”
2000g:05026 05B05
Webb, Bridget S. (4-OPEN-PM; Milton Keynes)

*Infinite**designs**with**more**point**orbits**than**block**orbits*. ... Summary: “Block’s lemma states that every automorphism group of a finite 2-(v,k, 4)*design*acts*with*at least as many*block**orbits*as*point**orbits*: this is not the case for*infinite**designs*. ...##
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Infinite linear spaces

1994
*
Discrete Mathematics
*

The only possibility of failure is if, at some stage, t

doi:10.1016/0012-365x(92)00503-j
fatcat:o4pmvw6czffqhhsayiu7wddq34
*points*are already incident*with**more**than*I*blocks*(or dually -it is enough to consider this case). ... So let (X,&J) be such a system,*with*any*block*incident*with*k*points*and any t*points*incident*with*a unique*block*. ...##
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Block transitive Steiner systems with more than one point orbit

2004
*
Journal of combinatorial designs (Print)
*

In particular, there is a 2-(ℵ 0 , 4, 1)

doi:10.1002/jcd.20018
fatcat:smtf5tzoxnextmykdtbjlw3xfu
*design**with*a*block*-transitive group of automorphisms having two*point**orbits*. This answers a question of P. J. Cameron and C. E. Praeger. ... For all 'reasonable' finite t, k and s we construct a t-(ℵ 0 , k, 1)*design*and a group of automorphisms which is transitive on*blocks*and has s*orbits*on*points*. ... Thus, the smallest case where we might have s > 1 is a 2-(∞, 4, 1)*design*and G*block*transitive*with*2*point**orbits*. In this case, each*block*contains exactly 2*points*from each*orbit*. ...##
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Sporadic neighbour-transitive codes in Johnson graphs

2013
*
Designs, Codes and Cryptography
*

We construct an additional five neighbour-transitive codes

doi:10.1007/s10623-013-9853-0
fatcat:rvji5owmobdijkqtso7f5sahv4
*with*minimum distance two admitting such a group. All 27 codes are t-*designs**with*t at least two. ... Johnson graphs J(v, k) of minimum distance at least three which admit a neighbour-transitive group of automorphisms that is an almost simple two-transitive group of degree v and does not occur in an*infinite*... All other intransitive maximal subgroups have either*more**than*2*orbits*or are not transitive on γ × γ, so do not give rise to any*more*examples. ...##
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A study on global stabilization of periodic orbits in discrete-time chaotic systems by using symbolic dynamics

2015
*
Kybernetika (Praha)
*

We find that a state x ∈ X is a T -periodic

doi:10.14736/kyb-2015-1-0004
fatcat:ghul63xggfgqrcjfo45pulzva4
*point*if and only if the sequence ρ ∈ Σ corresponding to x consists of*infinitely*repeated T -length*blocks*of symbols. ... Periodic*orbits*and the stability ρ = Ψ(x) = · · · s 1 s 2 · · · s T T -length*block*s 1 s 2 · · · s T T -length*block*· · · , which means that all periodic*orbits*in the invariant set can be specified ...##
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Page 5306 of Mathematical Reviews Vol. , Issue 2000h
[page]

2000
*
Mathematical Reviews
*

They call a

*design**with**more**than*one short*block*“singular”. They prove that a singular abelian 1-rotational Steiner*design**with**block*size k requires that the number of*points*be k? ... A |-rotational*design*is a balanced incomplete*block**design**with*a group G acting regularly on v — 1*points*. ...##
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Searching for line transitive, point imprimitive, linear spaces
[article]

2006
*
arXiv
*
pre-print

A finite linear space is a finite set of

arXiv:math/0604532v1
fatcat:uurx6qrgtvd5bpqylr3cyy3g3y
*points*and lines, where any two*points*lie on a unique line. Well known examples include projective planes. ...*Point*imprimitive spaces admit a second structure on the*points*aside from the lines, which is also preserved by an automorphism group. ... In both cases the search returned a negative result, indicating that no G-*point*imprimitive and G-line transitive*designs*exist conforming to either parameter set. ...##
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Ab initio downfolding based on the GW approximation for infinite-layer nickelates
[article]

2022
*
arXiv
*
pre-print

As a result, the correlation effect becomes

arXiv:2202.03661v1
fatcat:3eszzexa6retjetqknb75onnyu
*more*significant*than*that in the model constructed by the LDA-based downfolding. ... We derive an effective three-*orbital*model for the*infinite*-layer nickelates based on the band structure obtained by the GW approximation (GWA), where we consider the Ni 3d_x^2-y^2 and O 2p*orbitals*forming ... We note that there is a proposal that the electron pocket at the A*point*can be eliminated by*designing*a different type of the*block*layer [33] . ...##
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Delandtsheer–Doyen parameters for block-transitive point-imprimitive 2-designs
[article]

2020
*
arXiv
*
pre-print

Delandtsheer and Doyen bounded, in terms of the

arXiv:2009.00282v1
fatcat:fdq5s6x32jfvhbfaoedhd7pxnm
*block*size, the number of*points*of a*point*-imprimitive,*block*-transitive 2-*design*. ... To do this they introduced two integer parameters, m and n, now called Delandtsheer--Doyen parameters, linking the*block*size*with*the parameters of an associated imprimitivity system on*points*. ... invariant any non-trivial partition of the*point*set (a partition*with**more**than*one class and class size at least 2). ...##
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Global stabilization of periodic orbits in chaotic systems by using symbolic dynamics

2008
*
IFAC Proceedings Volumes
*

This work is the first attempt to systematically

doi:10.3182/20080706-5-kr-1001.02559
fatcat:ylpnsruutzaohpdshh7mhy3ecm
*design*a control system based on symbolic dynamics in the sense that one estimates the magnitude of control inputs and analyzes the Lyapunov stability. ... A periodic*orbit*is assigned as a target by giving a sequence in which symbols have periodicity. ... A state x ∈ X is a T -periodic*point*if and only if the sequence ρ ∈ Σ corresponding to x consists of*infinitely*repeated T -length*blocks*of symbols. ρ =Ψ(x)=··· s 1 s 2 ···s T From this proposition, ...##
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Ab initio Materials Design of Superconductivity in d^9 Nickelates
[article]

2022
*
arXiv
*
pre-print

Motivated by the recent theoretical materials

arXiv:2205.00239v1
fatcat:5hdqexhmnfhe7cwgjsxccyxw2e
*design*of superconducting d^9 nickelates for which the charge transfer from the NiO_2 to the*block*layer is completely suppressed [M. ... B 101, 075107 (2020)], we perform a calculation based on the dynamical vertex approximation and obtain the phase diagram of RbCa_2NiO_3 and A_2NiO_2Br_2 where A is a cation*with*a valence of 2.5+. ... ACKNOWLEDGMENTS We are grateful for fruitful discussions*with*Karsten Held, Liang Si, Paul Worm, Terumasa Tadano, Takuya Nomoto, and Kazuma Nakamura. ...##
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Mini-bandstructure tailoring in π-conjugated periodic block copolymers using the envelope crystalline-orbital method

2010
*
International Journal of Quantum Chemistry
*

A strategy for the systematic

doi:10.1002/qua.22715
fatcat:ibj75jdsinbfthlt6bqc7l26nq
*design*of polymeric superlattices*with*tailor-made mini-bandgaps and carrier mini-effective masses is described and computationally implemented by means of an envelope crystalline-*orbital*... from the lengths of the*blocks*. ... Summary, Conclusions and Perspectives*With*the aid of the envelope molecular-*orbital*theory, molecular organic quantum-dot superlattices*with*the general structure (PDA x -PPP y ) n were*designed*specifically ...##
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Even-freeness of cyclic 2-designs
[article]

2012
*
arXiv
*
pre-print

We prove the existence of

arXiv:1210.7516v1
fatcat:otp3xpspdfb3dg3cf6ilso53fq
*infinitely*many nontrivial Steiner 2-*designs*of large*block*size which have the cyclic automorphisms and higher even-freeness*than*the trivial lower bound but are not the*points*... A Steiner 2-*design*of*block*size k is an ordered pair (V, B) of finite sets such that B is a family of k-subsets of V in which each pair of elements of V appears exactly once. ... Because no pair of*points*appear*more**than*once in a Steiner 2-*design*, it is straightforward to see that every S(2, k, v) is k-even-free. ...##
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Orbits on points and lines in finite linear and quasilinear spaces

1987
*
Journal of combinatorial theory. Series A
*

., we prove that there exists a finite linear space whose automorphism group has exactly rr

doi:10.1016/0097-3165(87)90069-0
fatcat:volocgki2jfm5hn2zwvzzctbrm
*orbits*on*points*and i.*orbits*on lines if and only if rr;;; i.. < 19~7 Arndcmic Press. Inc. ... closed disc in the Euclidean plane and let S be the linear space whose*points*are the*points*of D and whose lines are the intersections of D*with*the lines of the plane having*more**than*one*point*in common ... If S is finite, a classical result of*Block*[ 1 ] asserts that n r ~ ). r· This is no longer true if S is*infinite*, as shown by the following example due to Valctte (see Buekenhout [3] ): let D be a ...
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