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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.  ...  Therefore L has orbits of length |L| = q n (q n − 1) on the set of blocks not containing ∞, that is the residual design. If X is an H -orbit on X then X contains a T -orbit B .  ... 
doi:10.1016/j.jcta.2010.10.007 fatcat:x6met46akrdo3drftaic3nxmne

Page 7320 of Mathematical Reviews Vol. , Issue 97M [page]

1997 Mathematical Reviews  
When v is finite it is well known that block-transitivity implies point- transitivity, whereas for infinite designs the relationship between the numbers of point and block orbits is unknown.  ...  Kestenband (1-NYIT; Old Westbury, NY) 97m:05024 05B05 Webb, Bridget S. (4-EXTR; Exeter) Orbits of infinite block designs. (English summary) Discrete Math. 169 (1997), no. 1-3, 287-292.  ... 

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.  ... 

An orbit theorem for Steiner triple systems

Peter J. Cameron
1994 Discrete Mathematics  
An automorphism group of a nontrivial (possibly infinite) Steiner triple system has at least as many block-orbits as point-orbits.  ...  The proof is a translation of that in the finite case, with a small twist. For block size 4, the argument fails, and, indeed, the stronger statement (involving block-tactical decompositions) is false.  ...  Clearly, the orbits of a group of automorphisms form a block-tactical decomposition.  ... 
doi:10.1016/0012-365x(94)90148-1 fatcat:kbfroxrckzcqvlolxps4cgwbfa

Efficient Two-Stage Group Testing Algorithms for DNA Screening [article]

Michael Huber
2011 arXiv   pre-print
Building on recent work by Levenshtein (2003) and Tonchev (2008), we construct in this paper new infinite classes of combinatorial structures, the existence of which are essential for attaining the minimum  ...  number of individual tests at the second stage of a two-stage disjunctive testing algorithm.  ...  If the length of an orbit is v, then the orbit is said to be full, otherwise short. A block chosen arbitrarily from an orbit is called a base block (or starter block ).  ... 
arXiv:1106.3680v1 fatcat:zeirq6mmrbewjpyfk54tbj34ge

Efficient Two-Stage Group Testing Algorithms for Genetic Screening

Michael Huber
2013 Algorithmica  
Building on recent work by Levenshtein (2003) and Tonchev (2008), several new infinite classes of such combinatorial designs are presented.  ...  The main focus is on novel combinatorial constructions in order to minimize the number of individual tests at the second stage of a two-stage disjunctive testing procedure.  ...  Acknowledgments The author thanks the anonymous referees for their careful reading and suggestions that helped improving the presentation of the paper.  ... 
doi:10.1007/s00453-013-9791-2 fatcat:xgleqxnr7fgwhkshrwdvnnhl7y

An infinite class of 5-designs

W.O Alltop
1972 Journal of combinatorial theory. Series A  
Q-C@) is called a t+, k, h) design provided / Q I = v and 9 is a family of k-subsets of Q such that every r-subset of Q is contained in exactly ,I members of 9.  ...  Such a design can always be extended to a j-design.  ...  Nonetheless, infinitely many Cdesigns are known (see [l] ). In Section 2, we shall give some essential properties of two of the 3-designs obtained from orbits under the affine group AF(n, 2).  ... 
doi:10.1016/0097-3165(72)90104-5 fatcat:vxew3zi7bzgnfkqdb5h6vfoxxu

An infinite class of 4-designs

W.O. Alltop
1969 Journal of Combinatorial Theory  
In order to show that S~ is contained in at least five members of ~ we define the following four members of G: o~+1 consists of exactly (q-2)/6 orbits of size (q + 1)q(q-1)/4, and we have a 4-design with  ...  Hence, each orbit in ~ contains at most (q + 1) q(q --1)/4 blocks. Thus, b ~< (q 4q-1 ) where b=]~].  ... 
doi:10.1016/s0021-9800(69)80096-7 fatcat:gr3k2nn63ng7bcxuhmensher4q

Block transitive Steiner systems with more than one point orbit

David M. Evans
2004 Journal of combinatorial designs (Print)  
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.  ...  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.  ...  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

Edge effects in finite elongated graphene nanoribbons

Oded Hod, Juan E. Peralta, Gustavo E. Scuseria
2007 Physical Review B  
We find that for hydrogen terminated graphene nanoribbons most of the physical features appearing in the density of states of an infinite graphene nanoribbon are recovered at a length of 40 nm.  ...  Our results indicate that careful consideration of finite-size and edge effects should be applied when designing new nanoelectronic devices based on graphene nanoribbons.  ...  capabilities 12 needed for electronic component design.  ... 
doi:10.1103/physrevb.76.233401 fatcat:vrgaxgoeijewdbitwz6mrfq2vy

Sporadic neighbour-transitive codes in Johnson graphs

Max Neunhöffer, Cheryl E. Praeger
2013 Designs, Codes and Cryptography  
group of degree v and does not occur in an infinite family of two-transitive groups.  ...  All 27 codes are t-designs with t at least two.  ...  The group G has two orbits on the 132 blocks of the Witt 5-(12, 6, 1) design, of lengths 22 and 110, and the subgroups H 1 , H 2 are stabilisers of blocks in these orbits.  ... 
doi:10.1007/s10623-013-9853-0 fatcat:rvji5owmobdijkqtso7f5sahv4

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.  ...  This demonstrates that the electron correlations play an essential role in nickelate superconductors and we can control them by changing block layers.  ...  A part of the calculation has been done on MASAMUNE-IMR of the Center for Computational Materials Science, Tohoku University.  ... 
arXiv:2205.00239v1 fatcat:5hdqexhmnfhe7cwgjsxccyxw2e

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.  ...  We explore extreme cases where these bounds are attained, give a new construction for a family of designs achieving these bounds, and pose several open questions concerning the Delandtsheer--Doyen parameters  ...  We consider 2-(v, k, λ) designs: these are structures D = (P, B) with two types of objects called points (elements of P) and blocks (elements of B, sometimes called lines).  ... 
arXiv:2009.00282v1 fatcat:fdq5s6x32jfvhbfaoedhd7pxnm

Infinite linear spaces

Peter J. Cameron
1994 Discrete Mathematics  
Elementary cardinal arithmetic shows that, if the number of point-orbits is infinite, then the number of line-orbits is at least as great.  ...  Any infinite linear space with constant finite block size can be extended anyfinite number of times. q  ... 
doi:10.1016/0012-365x(92)00503-j fatcat:o4pmvw6czffqhhsayiu7wddq34

Weakly union-free twofold triple systems

Yeow Meng Chee, Charles J. Colbourn, Alan C. H. Ling
1997 Annals of Combinatorics  
In this paper, we settle a problem of Frankl and Filredi, which is a special case of a problem of Erdt~s, determining the maximum number of hyperedges in a 3-uniform hypergraph in which no two pairs of  ...  The extremal case corresponds to the existence of weakly union-free twofold triple systems, which is settled here with six definite and four possible exceptions.  ...  A set of representatives of these orbits forms a set of starter blocks for the 3-GDD.  ... 
doi:10.1007/bf02558476 fatcat:mth7h5q5ancr7irj7xiue7puoa
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