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There exists no symmetric configuration with 33 points and line size 6

2007
*
The Australasian Journal of Combinatorics
*

Ö× ´Ú Ö µ ÓÒ× ×Ø× Ó × Ø Ó Ú ÔÓ ÒØ×¸ × Ø Ó Ð Ò ×¸ Ò Ò Ò Ò Ö Ð Ø ÓÒ ØÛ Ò ÔÓ ÒØ× Ò Ð Ò × ×Ù Ø Ø ´½µ Ú ÖÝ ÔÓ ÒØ × Ò ÒØ Û Ø Ö Ð Ò ×¸´¾µ Ú ÖÝ Ð Ò × Ò ÒØ Û Ø ÔÓ ÒØ×¸ Ò ´¿µ ÒÝ ØÛÓ ×Ø Ò Ø ÔÓ ÒØ× Ö Ò ÒØ Û Ø Ø

dblp:journals/ajc/KaskiO07
fatcat:fvbwlgcre5fo3hmrwcqlahga4y
*ÑÓ*... Ò Ø ½× Ò Ø Ò Ò Ò Ó ÔÓ ÒØ Û Ø Ð Ò º Ì ÓÒ×ØÖ ÒØ× ´½µ¸´¾µ¸ Ò ´¿µ Ö ÕÙ Ú Ð ÒØ ØÓ Ö ÕÙ Ö Ò Ø Ø ´½¼ µ Ú ÖÝ ÖÓÛ ×ÙÑ× ØÓ Ö¸Ø Ø ´¾¼ µ Ú ÖÝ ÓÐÙÑÒ ×ÙÑ× ØÓ ¸ Ò Ø Ø ´¿¼ µ Ø ÒÒ Ö ÔÖÓ Ù Ø Ó ÒÝ Ø ÛÓ ×Ø Ò Ø ÖÓÛ× × Ø*ÑÓ*...##
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Research problem

1994
*
Discrete Mathematics
*

Readers wishing to make comments dealing

doi:10.1016/0012-365x(94)90045-0
fatcat:gsqq2emgr5asrezq6cqghvobze
*with*technical matters about a problem that has appeared should write to the correspondent for that particular problem. ... References Apart from the general theorem in [2]*there*are only two further non-*existence*results for*symmetric**configurations*uk:*there*is*no**configuration*326 [*6*]*and**there*is*no**configuration*749 ... Background: Compare the*existence*table of*symmetric**configurations*in [4] .*There*is*no**configuration*437 (a projective plane of order*6*).*There*is*no**configuration*44,. ...##
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Configurations and graphs

1993
*
Discrete Mathematics
*

.,

doi:10.1016/0012-365x(93)90162-m
fatcat:lm3o7ocvpjcp7ehr7tmaof4lci
*Configurations**and*graphs, Discrete Mathematics 111 (1993) 269-276. ... In the first part the analogy between*configurations**and*regular bipartite graphs is described. Some instances of parallel research in graph theory*and**configuration*theory are mentioned. ... A con$guration (v,, bk) is a finite incidence structure*with*the following properties: (1)*There*are v*points**and*b*lines*. (2)*There*are k*points*on each*line**and*r*lines*through each*point*. (3) Two different ...##
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The Largest Pure Partial Planes of Order 6 Have Size 25

2018
*
Electronic Journal of Combinatorics
*

In this paper, we prove that the largest pure partial plane of order

doi:10.37236/6473
fatcat:yxhtpqt7s5fsvpopuiwklhbkoq
*6*has*size*25. At the same time, we classify all pure partial planes of order*6**and**size*25 up to isomorphism. ... For the remaining cases, we subdivide each search by phases*and*use multiple checks to reduce search space via symmetry. ... In [10] , McCarthy et al. proved that*there*are*no*pure partial planes of order*6**and**size*29*with*very long combinatorial arguments. However, the exact maximum has not been given. ...##
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Nonsymmetric configurations with natural index

1994
*
Discrete Mathematics
*

By using results about resolvable

doi:10.1016/0012-365x(94)90087-6
fatcat:j3rgfrcocfdk3b2hson7hqkwli
*and*near-resolvable Steiner systems as well as difference triangle sets, the*existence*of all*configurations**with*k = 3 is proved. ... The*configuration*graph of a*configuration*(u" bk) has the v*points*as vertices,*and*two vertices are connected by an edge if they are not collinear in the*configuration*. ... For k =*6*not all possible Steiner systems*exist*.*There*is*no*S (2,*6*, 36) ,*and*affine plane of order*6*. This may be a special case. ...##
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Finite linear spaces consisting of two symmetric configurations

2005
*
Glasnik Matematicki - Serija III
*

A question whether any Steiner 2-design

doi:10.3336/gm.40.1.13
fatcat:miv2gfqwljbeln23hgvj2advqm
*with*twice as many*lines*as*points*belongs to this family of linear spaces is raised,*and*answered in the affirmative for all known examples of such designs. 2000 ... We investigate finite linear spaces consisting of two*symmetric**configurations*. A construction method using projective planes is presented, giving a possibly infinite number of examples. ... Provided*there**exist*projective planes of order m*and*of order n,*with*n = m 2 + m + 1 or n = m 2 + m + 2,*there**exists*a TSC space for (m + 1, n). ...##
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Page 7609 of Mathematical Reviews Vol. , Issue 2000k
[page]

2000
*
Mathematical Reviews
*

Summary: “(r,1)-designs are linear spaces

*with*v*points*where every*point*lies on exactly r*lines*. ... Math. 99 (2000),*no*. 1-3, 401-411. Summary: “*Symmetric**configurations*n3 are equivalent to the bicubic graphs of girth >*6*. ...##
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Questioning the existence of a unique ground-state structure for Si clusters

2007
*
Physical Review B
*

Isotope pure

doi:10.1103/physrevb.75.085411
fatcat:6fwgynrrarf27jobg55vriu26q
*configurations**with*rotational symmetry*and**symmetric**configurations*containing one additional isotope are disfavored by these effects. ... Density functional*and*quantum Monte Carlo calculations challenge the*existence*of a unique ground-state structure for certain Si clusters. ... Zeng*and*A. ...##
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Strongly regular configurations
[article]

2021
*
arXiv
*
pre-print

We study combinatorial

arXiv:2104.04880v2
fatcat:ayh7dvpanndjvoghctbaadxcjm
*configurations**with*the associated*point**and**line*graphs being strongly regular. ... Necessary*existence*conditions are proved*and*a table of feasible parameters of such*configurations**with*at most 200*points*is presented. ... The*points*non-collinear*with*both P*and*Q are the intersections of one of the*lines*AP , BP , CP*with*one of the*lines*AQ, BQ, CQ;*there*are*6*such*points*. ...##
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Tables of parameters of symmetric configurations v_k
[article]

2014
*
arXiv
*
pre-print

Tables of the currently known parameters of

arXiv:1312.3837v2
fatcat:zhxdapdv7fbkvnjwkk2cojqooi
*symmetric**configurations*are given. Formulas for parameters of the known infinite families of*symmetric**configurations*are presented as well. ... IV], [38, Tab. 2], [56, Tab. 1a], [61] Table*6*. 1 . 61 Theorem 6.1. [*33*, Th. 2.4]*There*is*no**symmetric**configuration*(k 2 Table 4 .2. 4 Table*6*. 1 . 61 Values of v for which a cyclic*symmetric*... [36] (i) A*configuration*(v r , b k ) is an incidence structure of v*points**and*b*lines*such that each*line*contains k*points*, each*point*lies on r*lines*,*and*two distinct*points*are connected by at ...##
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On some operations on finite affine planes applied to the theory of regular configurations

2010
*
Demonstratio Mathematica
*

We prove that the Pappos–Pascal

doi:10.1515/dema-2013-0221
fatcat:ssrblyfcjbffdhsxmiiiw6xhhm
*configuration*is the B-contraction of the affine plane of order 4*and*we relate it to the Havliček–Tietze*configuration*. We present a new (HT) ... AbstractWe consider some operations on affine planes which resemble the construction of a derived affine plane at a*point*of the Benz plane. ...*There**exists*a*configuration*C t k = ((k + tk − 2)k tk , tk(k + tk − 2) k )*with*a natural index t*and*the*size*of*line*k, provided*there*is an affine plane of order n = k + tk − 1. Proof. ...##
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Page 4707 of Mathematical Reviews Vol. , Issue 93i
[page]

1993
*
Mathematical Reviews
*

Tamas Szényi (Budapest)
93i:05015 05B05 05B25 51E05
Bierbrauer, Jiirgen (D-HDBG)
Designs

*with*block-*size**6*in projective planes of characteristic 2. ... The author considers the action of the group 05B Designs*and**configurations*93i:05018 G = PGL(3, g) on PG(2, q),*and*the orbits of G on*6*-sets are given. ...##
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Codes and matrices in studies on designs

1989
*
Discrete Applied Mathematics
*

This paper investigates methods based on codes

doi:10.1016/0166-218x(92)90280-n
fatcat:ty5dlbmvs5ce7p7sgu4wqhaxwa
*and*matrices for determming the*existence*or nonexistence of designs. ... Jr., Roth, ban Rees*and*C'ansrnnr. An early paper by Hamada*and*Kobayslu made the first steps in thts direction. ... The weight distribution is now completely determined*and*in particular A 19-24,675. For a word of weight 19 the*configuration*consists of*6**lines**with*5*points*of the 19*and*37*lines**with*3*points*. ...##
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Does monocular visual space contain planes?

2010
*
Acta Psychologica
*

The issue of the

doi:10.1016/j.actpsy.2009.12.002
pmid:20053390
fatcat:2sefz3igizfiflumtsi5hrnftu
*existence*of planes-understood as the carriers of a nexus of straight*lines*-in the monocular visual space of a stationary human observer has never been addressed. ... The most recent empirical data apply to binocular visual space*and*date from the 1960s (Foley, 1964 ). This appears to be both the first*and*the last time this basic issue was addressed empirically. ... From left to right, top to bottom, these are subtasks #1, #2 (*symmetrical*pair), subtasks #3, #4 (*symmetrical*pair), subtasks #5, #*6*(*symmetrical*pair), subtasks #7, #8 (*symmetrical*pair). ...##
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Mobile icosapods

2017
*
Advances in Applied Mathematics
*

In 1904, Borel designed a technique to construct examples of such 20-pods, but could not constrain the legs to have base

doi:10.1016/j.aam.2016.12.002
fatcat:nkpalu6jbfck7didcibhoucvsu
*and*platform*points**with*real coordinates. ... We show that Borel's construction yields all mobile 20-pods,*and*that it is possible to construct examples*with*all real coordinates. ... We also thank Charles Wampler for*pointing*us at several references. ...
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