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

Petteri Kaski, Patric R. J. Östergård
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 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  ... 
dblp:journals/ajc/KaskiO07 fatcat:fvbwlgcre5fo3hmrwcqlahga4y

Research problem

1994 Discrete Mathematics  
Readers wishing to make comments dealing 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,.  ... 
doi:10.1016/0012-365x(94)90045-0 fatcat:gsqq2emgr5asrezq6cqghvobze

Configurations and graphs

Harald Gropp
1993 Discrete Mathematics  
., 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  ... 
doi:10.1016/0012-365x(93)90162-m fatcat:lm3o7ocvpjcp7ehr7tmaof4lci

The Largest Pure Partial Planes of Order 6 Have Size 25

Yibo Gao
2018 Electronic Journal of Combinatorics  
In this paper, we prove that the largest pure partial plane of order 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.  ... 
doi:10.37236/6473 fatcat:yxhtpqt7s5fsvpopuiwklhbkoq

Nonsymmetric configurations with natural index

Harald Gropp
1994 Discrete Mathematics  
By using results about resolvable 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.  ... 
doi:10.1016/0012-365x(94)90087-6 fatcat:j3rgfrcocfdk3b2hson7hqkwli

Finite linear spaces consisting of two symmetric configurations

Vedran Krcadinac
2005 Glasnik Matematicki - Serija III  
A question whether any Steiner 2-design 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).  ... 
doi:10.3336/gm.40.1.13 fatcat:miv2gfqwljbeln23hgvj2advqm

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.  ... 

Questioning the existence of a unique ground-state structure for Si clusters

Waldemar Hellmann, R. G. Hennig, Stefan Goedecker, C. J. Umrigar, Bernard Delley, T. Lenosky
2007 Physical Review B  
Isotope pure 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.  ... 
doi:10.1103/physrevb.75.085411 fatcat:6fwgynrrarf27jobg55vriu26q

Strongly regular configurations [article]

Marién Abreu, Martin Funk, Vedran Krčadinac, Domenico Labbate
2021 arXiv   pre-print
We study combinatorial 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.  ... 
arXiv:2104.04880v2 fatcat:ayh7dvpanndjvoghctbaadxcjm

Tables of parameters of symmetric configurations v_k [article]

Alexander A. Davydov, Giorgio Faina, Massimo Giulietti, Stefano Marcugini, Fernanda Pambianco
2014 arXiv   pre-print
Tables of the currently known parameters of 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  ... 
arXiv:1312.3837v2 fatcat:zhxdapdv7fbkvnjwkk2cojqooi

On some operations on finite affine planes applied to the theory of regular configurations

Hanna Makowiecka
2010 Demonstratio Mathematica  
We prove that the Pappos–Pascal 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.  ... 
doi:10.1515/dema-2013-0221 fatcat:ssrblyfcjbffdhsxmiiiw6xhhm

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.  ... 

Codes and matrices in studies on designs

Marshall Hall
1989 Discrete Applied Mathematics  
This paper investigates methods based on codes 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.  ... 
doi:10.1016/0166-218x(92)90280-n fatcat:ty5dlbmvs5ce7p7sgu4wqhaxwa

Does monocular visual space contain planes?

Jan J. Koenderink, Liliana Albertazzi, Andrea J. van Doorn, Raymond van Ee, Wim A. van de Grind, Astrid M.L. Kappers, Joe S. Lappin, J. Farley Norman, A.H.J. (Stijn) Oomes, Susan P. te Pas, Flip Phillips, Sylvia C. Pont (+4 others)
2010 Acta Psychologica  
The issue of the 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).  ... 
doi:10.1016/j.actpsy.2009.12.002 pmid:20053390 fatcat:2sefz3igizfiflumtsi5hrnftu

Mobile icosapods

M. Gallet, G. Nawratil, J. Schicho, J.M. Selig
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 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.  ... 
doi:10.1016/j.aam.2016.12.002 fatcat:nkpalu6jbfck7didcibhoucvsu
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