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On the falsity of a conjecture on orthogonal steiner triple systems

Alexander Rosa
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).  ... 
doi:10.1016/0097-3165(74)90078-8 fatcat:3eafemh3kna3fdoapay5ttodkm

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

J. I. Hall
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.  ... 
doi:10.21915/bimas.2019203 fatcat:7txe5dtcnngtzobnugwkhnnguu

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

Aloke Dey
Special Proceedings of 19 th Annual Conference of SSCA held at SKUAST, Jammu during   unpublished
Two Latin squares 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.  ... 
fatcat:cx3h2ulnavgpvbw3cpolxma2m4

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

Aloke Dey
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,  ... 
fatcat:xkwnvxcm5bdh5i6o7euk3yxxcq

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

R. A. Cuninghame-Green, A. Schrijver
1980 Journal of the Operational Research Society  
bound, Wilson's existence theory for designs, Lovasz's results 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.  ... 
doi:10.2307/2581088 fatcat:szdtpgrkzrfvvehhovqz3r6vxq

From Euclid to Riemann and Beyond [article]

Toshikazu Sunada
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.  ... 
arXiv:1904.01845v1 fatcat:tyckpaulw5agfbzj7zelbk5htm

An episodic history of mathematics: mathematical culture through problem solving

2010 ChoiceReviews  
Pythagorean 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.  ... 
doi:10.5860/choice.48-1529 fatcat:r52umdi4vja6bfxb7kmudrn4ui

Ambiguity and Ambiguity Aversion [chapter]

Mark J. Machina, Marciano Siniscalchi
2014 Handbook of the Economics of Risk and Uncertainty  
It goes 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).  ... 
doi:10.1016/b978-0-444-53685-3.00013-1 fatcat:gsw3lpjew5gq7d6lgpm7zxdqey

Ambiguity and Ambiguity Aversion [chapter]

Marciano Siniscalchi
2008 The New Palgrave Dictionary of Economics  
It goes 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).  ... 
doi:10.1057/978-1-349-95121-5_2439-1 fatcat:e7sr3z7nfjfxffikn7dzhd7npm
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