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Unifying some known infinite families of combinatorial 3-designs

Masakazu Jimbo, Yuta Kunihara, Reinhard Laue, Masanori Sawa
2011 Journal of combinatorial theory. Series A  
Those resolvable 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.  ... 
doi:10.1016/j.jcta.2010.10.007 fatcat:x6met46akrdo3drftaic3nxmne

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.  ... 

Infinite linear spaces

Peter J. Cameron
1994 Discrete Mathematics  
The only possibility of failure is if, at some stage, t 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.  ... 
doi:10.1016/0012-365x(92)00503-j fatcat:o4pmvw6czffqhhsayiu7wddq34

Block transitive Steiner systems with more than one point orbit

David M. Evans
2004 Journal of combinatorial designs (Print)  
In particular, there is a 2-(ℵ 0 , 4, 1) 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.  ... 
doi:10.1002/jcd.20018 fatcat:smtf5tzoxnextmykdtbjlw3xfu

Sporadic neighbour-transitive codes in Johnson graphs

Max Neunhöffer, Cheryl E. Praeger
2013 Designs, Codes and Cryptography  
We construct an additional five neighbour-transitive codes 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.  ... 
doi:10.1007/s10623-013-9853-0 fatcat:rvji5owmobdijkqtso7f5sahv4

A study on global stabilization of periodic orbits in discrete-time chaotic systems by using symbolic dynamics

Masayasu Suzuki, Noboru Sakamoto
2015 Kybernetika (Praha)  
We find that 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.  ...  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  ... 
doi:10.14736/kyb-2015-1-0004 fatcat:ghul63xggfgqrcjfo45pulzva4

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.  ... 

Searching for line transitive, point imprimitive, linear spaces [article]

Gregory Cresp
2006 arXiv   pre-print
A finite linear space is a finite set of 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.  ... 
arXiv:math/0604532v1 fatcat:uurx6qrgtvd5bpqylr3cyy3g3y

Ab initio downfolding based on the GW approximation for infinite-layer nickelates [article]

Motoaki Hirayama, Yusuke Nomura, Ryotaro Arita
2022 arXiv   pre-print
As a result, the correlation effect becomes 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] .  ... 
arXiv:2202.03661v1 fatcat:3eszzexa6retjetqknb75onnyu

Delandtsheer–Doyen parameters for block-transitive point-imprimitive 2-designs [article]

Carmen Amarra, Alice Devillers, Cheryl E. Praeger
2020 arXiv   pre-print
Delandtsheer and Doyen bounded, in terms of the 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).  ... 
arXiv:2009.00282v1 fatcat:fdq5s6x32jfvhbfaoedhd7pxnm

Global stabilization of periodic orbits in chaotic systems by using symbolic dynamics

Masayasu Suzuki, Noboru Sakamoto
2008 IFAC Proceedings Volumes  
This work is the first attempt to systematically 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,  ... 
doi:10.3182/20080706-5-kr-1001.02559 fatcat:ylpnsruutzaohpdshh7mhy3ecm

Ab initio Materials Design of Superconductivity in d^9 Nickelates [article]

Motoharu Kitatani, Yusuke Nomura, Motoaki Hirayama, Ryotaro Arita
2022 arXiv   pre-print
Motivated by the recent theoretical materials 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.  ... 
arXiv:2205.00239v1 fatcat:5hdqexhmnfhe7cwgjsxccyxw2e

Mini-bandstructure tailoring in π-conjugated periodic block copolymers using the envelope crystalline-orbital method

C. A. Mujica-Martínez, J. C. Arce
2010 International Journal of Quantum Chemistry  
A strategy for the systematic 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  ... 
doi:10.1002/qua.22715 fatcat:ibj75jdsinbfthlt6bqc7l26nq

Even-freeness of cyclic 2-designs [article]

Yuichiro Fujiwara
2012 arXiv   pre-print
We prove the existence of 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.  ... 
arXiv:1210.7516v1 fatcat:otp3xpspdfb3dg3cf6ilso53fq

Orbits on points and lines in finite linear and quasilinear spaces

Aart Blokhuis, Andries Brouwer, Ann Delandtsheer, Jean Doyen
1987 Journal of combinatorial theory. Series A  
., we prove that there exists a finite linear space whose automorphism group has exactly rr 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  ... 
doi:10.1016/0097-3165(87)90069-0 fatcat:volocgki2jfm5hn2zwvzzctbrm
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