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On the falsity of a conjecture on orthogonal steiner triple systems

1974
*
Journal of combinatorial theory. Series A
*

*A*pair

*of*

*orthogonal*

*Steiner*

*triple*

*systems*

*of*order v = 27 is constructed, thus showing

*the*

*conjecture*about

*the*non-existence

*of*

*a*pair

*of*

*orthogonal*

*Steiner*

*triple*

*systems*

*of*orders v = 3 (mod 6) to ... Two

*Steiner*

*triple*

*systems*(briefly STS) S, and S,

*on*

*the*same set S are said to be

*orthogonal*if (1) they are disjoint, i.e., have no

*triple*in common, and (2) if two pairs

*of*elements appear with

*the*...

*On*

*the*other hand, Mullin and Nemeth in [4] attribute

*the*following

*conjecture*to O'Shaughnessy [5] :

*CONJECTURE*. There does not exist

*a*pair

*of*

*orthogonal*STS

*of*order v for any v = 3 (mod 6). ...

##
###
Page 1872 of Mathematical Reviews Vol. 48, Issue 6
[page]

1974
*
Mathematical Reviews
*

Rosa, Alexander 10845

*On**the**falsity**of**a**conjecture**on**orthogonal**Steiner**triple**systems*. J. Combinatorial Theory Ser.*A*16 (1974), 126-128. ... Two*Steiner**triple**systems*(S, ¢,) and (S, t,) are said to be*orthogonal*provided they are disjoint (have no*triple*in common) and if two pairs*of*elements*of*S appear with*the*same third element in*triples*...##
###
Page 1378 of Mathematical Reviews Vol. , Issue 90C
[page]

1990
*
Mathematical Reviews
*

An oval is

*a*subset*of**the*points*of**a**Steiner**triple**system*which has*the*property that each point*of**the*oval lies*on*precisely*one*tangent (line meeting*the*oval in precisely*one*point) and no line ... nested*Steiner**triple**systems*and*Steiner*pentagon*systems*. ...##
###
Page 429 of Mathematical Reviews Vol. 22, Issue 4A
[page]

1961
*
Mathematical Reviews
*

*A*. J. Hoffman (New York) 2557 : Bose, R. C.; Shrikhande, 8. 8.

*On*

*the*construction

*of*sets

*of*mutually

*orthogonal*Latin squares and

*the*

*falsity*

*of*

*a*

*conjecture*

*of*Euler. Trans. Amer. Math. ...

*The*third section treats Latin squares and rectangles,

*Steiner*

*triple*

*systems*, and

*the*construction

*of*(or proof

*of*non-existence

*of*) various partially balanced incomplete block designs, especially

*the*...

##
###
Page 638 of Mathematical Reviews Vol. , Issue 96b
[page]

1996
*
Mathematical Reviews
*

*The*authors are able to prove

*the*

*falsity*

*of*both Euler’s and MacNeish’s

*conjectures*for arbitrary dimension. J. ...

*A*Mendelsohn

*triple*

*system*MTS(v,

*A*) is an ordered pair (V, B) where B is

*a*collection

*of*directed

*triples*{(

*a*,b),(b,c),(c,

*a*)}, where {

*a*,b,c} C V, such that each ordered pair in V x V is in ex- actly 4 ...

##
###
Page 3245 of Mathematical Reviews Vol. 58, Issue 5
[page]

1979
*
Mathematical Reviews
*

Shrikhande

*of**the**falsity**of*Euler’s*conjecture*;*the*basic properties*of*symmetric designs; and results*on**the*number*of*mutually*orthogonal*Latin squares. ... (*A**Steiner**triple**system**of*order 2¢+ 1 is indexed if it contains*a**Steiner**triple**system**of*order ¢.) ...##
###
Transposition Algebras

2019
*
Bulletin of the Institute of Mathematics Academia Sinica NEW SERIES
*

*The*topics discussed here had

*a*similar start. Algebras were introduced to aid in

*the*construction

*of*finite simple groups, particularly those that are sporadic. ... Later

*the*classification

*of*finite dimensional, complex, semisimple Lie algebras was in turn reduced (primarily by Weyl) to

*the*classification

*of*finite groups generated by Euclidean reflections. ... (iii)

*A*partial linear space (P, L) is

*a*partial

*triple*

*system*if every line is

*a*3-subset

*of*P; it is

*a*

*Steiner*

*triple*

*system*if it is additionally

*a*linear space. ...

##
###
The Problem of 36 Officers, Euler's Conjecture and Related Matters

*
Special Proceedings of 19 th Annual Conference of SSCA held at SKUAST, Jammu during
*
unpublished

Two Latin squares

fatcat:cx3h2ulnavgpvbw3cpolxma2m4
*of**the*same order are said to be*orthogonal*to each other if, when any*of**the*squares is superimposed*on**the*other, every ordered pair*of*symbols appears exactly once. ...*A*Latin square*of*order (or, side) s is an s s matrix (array) with entries from*a*set*of*s ≥ 2 distinct symbols (or, letters) such that each symbol appears in each row and each column precisely once. ...*Steiner*(1853) proposed*the*problem*of*arranging n objects in triplets (called*Steiner*"s*triple**systems*) such that every pair*of*objects appears in exactly*one*set. ...##
###
The Problem of 36 Ocers, Euler's Conjecture and Related Matters

unpublished

*The*New York Times in

*the*report also made

*the*following remark:

*The*three mathematicians who finally cracked

*the*problem are now known among their colleagues as Euler's Spoilers. ...

*Steiner*(1853) proposed

*the*problem

*of*arranging n objects in triplets (called Steiner's

*triple*

*systems*) such that every pair

*of*objects appears in exactly

*one*set. ...

*The*solution

*of*

*the*above problem (called

*the*Kirkman's schoolgirl problem) has

*a*

*one*-

*one*correspondence with

*the*solution

*of*

*a*BIB design and such

*a*BIB design is also called

*a*Kirkman

*Triple*

*System*, ...

##
###
Page 110 of Mathematical Reviews Vol. 25, Issue Index
[page]

*
Mathematical Reviews
*

(with Jungnickel, Dieter; Pott, Alexander) Symmetric divisible designs with k—

*A*,=1. 93b:05011 —*Falsity**of**a**conjecture**on*dicyclic designs. 93b:05012 Assaf, Ahmed M. ...*A*geometric construction*of**the**Steiner**system*S(4, 7,23). 93i:05014 Bagchi, Bhaskar (with Bagchi, Sunanda; Mukhopadhyay,*A*. C.) ...##
###
Packing and Covering in Combinatorics

1980
*
Journal of the Operational Research Society
*

bound, Wilson's existence theory for designs, Lovasz's results

doi:10.2307/2581088
fatcat:szdtpgrkzrfvvehhovqz3r6vxq
*on*perfect graphs, Kneser's*conjecture*and*the*Shannon capacity, Baranyai's theorem*on*partitions into partitions,*the*Cook-Karp theory*of*... NP-completeness,*the*solution by Duijvestijn*of**the*squared square problem,*the*results*of*McEliece, et al., and*of*Odlyzko and Sloane*on*codes and sphere-packings, and*the*Edmonds-Giles method for solving ... SHRIKHANDE, Further results*on**the*construction*of*mutually*orthogonal*Latin squares and*the**falsity**of*Euler's*conjecture*, Canad. J. Math. 12 (1960) 189-203. [2] S. CHOWLA, P. ERDOS & E.G. ...##
###
From Euclid to Riemann and Beyond
[article]

2019
*
arXiv
*
pre-print

*The*purpose

*of*this essay is to trace

*the*historical development

*of*geometry while focusing

*on*how we acquired mathematical tools for describing

*the*"shape

*of*

*the*universe." ... More specifically, our aim is to consider, without

*a*claim to completeness,

*the*origin

*of*Riemannian geometry, which is indispensable to

*the*description

*of*

*the*space

*of*

*the*universe as

*a*"generalized curved ... Acknowledgement I wish to thank my colleague Jim Elwood whose suggestions were very helpful for

*the*improvement

*of*

*the*first short draft

*of*this essay. ...

##
###
An episodic history of mathematics: mathematical culture through problem solving

2010
*
ChoiceReviews
*

Pythagorean

doi:10.5860/choice.48-1529
fatcat:r52umdi4vja6bfxb7kmudrn4ui
*Triples*It is natural to ask which*triples**of*integers (*a*, b, c) satisfy*a*2 + b 2 = c 2 . Such*a*trio*of*numbers is called*a*Pythagorean*triple*. ... This question has become known as*the*Poincaré*Conjecture*, and it is*one**of**the*most important questions*of*twentieth century mathematics. ...*The*variables x, y, z are*the*coordinates*of**a*point*on**the*body. ...##
###
Ambiguity and Ambiguity Aversion
[chapter]

2014
*
Handbook of the Economics of Risk and Uncertainty
*

It goes

doi:10.1016/b978-0-444-53685-3.00013-1
fatcat:gsw3lpjew5gq7d6lgpm7zxdqey
*on*to describe Ellsberg's classic urn paradoxes and*the*extensive experimental literature they have inspired. ... It continues with analytical descriptions*of**the*numerous (primarily axiomatic) models*of*ambiguity aversion which have been developed by economic theorists, and concludes with*a*discussion*of*some current ... utility with respect to*the**Steiner*point*of*P (*a*construct which generalizes*the*notion*of*center*of*gravity). ...##
###
Ambiguity and Ambiguity Aversion
[chapter]

2008
*
The New Palgrave Dictionary of Economics
*

It goes

doi:10.1057/978-1-349-95121-5_2439-1
fatcat:e7sr3z7nfjfxffikn7dzhd7npm
*on*to describe Ellsberg's classic urn paradoxes and*the*extensive experimental literature they have inspired. ... It continues with analytical descriptions*of**the*numerous (primarily axiomatic) models*of*ambiguity aversion which have been developed by economic theorists, and concludes with*a*discussion*of*some current ... utility with respect to*the**Steiner*point*of*P (*a*construct which generalizes*the*notion*of*center*of*gravity). ...
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