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Primary Jordan triple systems. III
Siberian Mathematical Journal, 1985In Part II [Sib. Mat. Zh. 25, No. 5(147), 50--61 (1984; Zbl 0562.17007)], the author classified the prime non-degenerate Jordan triple systems (Jordan pairs) which do not satisfy a certain system of polynomial identities \(G=0\). In this work he completes the classification of such systems (pairs) by showing his earlier results are still valid when the
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Communications in Algebra, 1990
Let V=V0: be a vector space over a field F wit11 associated spaces of linear functionals V1, V2, V3, V4, Vj belonging to Hom (Vj -1,F).In this paper we generalize the procedure used to extend a binary product on V to one on V2,focusing here on the case where V is a triple system.
Meighan I. Dillon, John A. Loustau
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Let V=V0: be a vector space over a field F wit11 associated spaces of linear functionals V1, V2, V3, V4, Vj belonging to Hom (Vj -1,F).In this paper we generalize the procedure used to extend a binary product on V to one on V2,focusing here on the case where V is a triple system.
Meighan I. Dillon, John A. Loustau
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Embeddings of pure mendelsohn triple systems and pure directed triple systems
Journal of Combinatorial Designs, 1995AbstractIt is proved in this article that the necessary and sufficient conditions for the embedding of a λ‐fold pure Mendelsohn triple system of order v in λ‐fold pure Mendelsohn triple of order u are λu(u − 1) ≡ 0 (mod 3) and u ⩾ 2v + 1. Similar results for the embeddings of pure directed triple systems are also obtained. © 1995 John Wiley & Sons,
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1999
Abstract In this chapter, we consider a second type of ordering: designs in which the blocks are cyclic triples. A Mendelsohn triple systemof order vand index λ is a pair (V, B). Vis a v-set of elementsand Bis a collection of cyclic triples on V;every ordered pair of distinct elements from Vappears in precisely λ of the cyclic triples of
Charles J Colbourn, Alexander Rosa
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Abstract In this chapter, we consider a second type of ordering: designs in which the blocks are cyclic triples. A Mendelsohn triple systemof order vand index λ is a pair (V, B). Vis a v-set of elementsand Bis a collection of cyclic triples on V;every ordered pair of distinct elements from Vappears in precisely λ of the cyclic triples of
Charles J Colbourn, Alexander Rosa
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Bicyclic directed triple systems
1998The paper is about directed triple systems \(\text{DTS}(v)\) which admit an automorphism with cycles of lengths \(N \leq M\), \(N+M = v\). It is proved that for \(N = M\) necessary and sufficient conditions for the existence of such a directed triple system can be expressed by \(v \equiv 4 \pmod 6\), while for ...
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Geometriae Dedicata, 1989
We prove the following result. Let S be a Steiner triple system embedded in the projective plane П of order n, such that r=n+1, and such that there exists a line l of Π exterior to S. Let G be a collineation group of Π fixing S, fixing l and transitive on the blocks of S.
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We prove the following result. Let S be a Steiner triple system embedded in the projective plane П of order n, such that r=n+1, and such that there exists a line l of Π exterior to S. Let G be a collineation group of Π fixing S, fixing l and transitive on the blocks of S.
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1999
Abstract In this and the next chapter, we examine extemions of designs (particularly triple systems), in which blocks are taken to contain orderedrather than unordered pairs. Vieprimarily consider two different types of ordered blocks.
Charles J Colbourn, Alexander Rosa
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Abstract In this and the next chapter, we examine extemions of designs (particularly triple systems), in which blocks are taken to contain orderedrather than unordered pairs. Vieprimarily consider two different types of ordered blocks.
Charles J Colbourn, Alexander Rosa
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2011
In this paper we present a new class of finite geometries (matroids) that have the same structural regularity found in the classical affine and projective geometries, and whose coordinatization by a class of Moufang loops provides illuminating links between geometric and algebraic concepts. A more detailed account of this work may be found in [9].
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In this paper we present a new class of finite geometries (matroids) that have the same structural regularity found in the classical affine and projective geometries, and whose coordinatization by a class of Moufang loops provides illuminating links between geometric and algebraic concepts. A more detailed account of this work may be found in [9].
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1997
Abstract Query 6 on page 48 of the Lady’s and Gentleman’s Diary for 1850 was posed by Kirkman as follows. Fifteen young ladies in a school walk out three abreast for seven days in succession: it is required to arrange them daily, so that no two shall walk twice abreast.
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Abstract Query 6 on page 48 of the Lady’s and Gentleman’s Diary for 1850 was posed by Kirkman as follows. Fifteen young ladies in a school walk out three abreast for seven days in succession: it is required to arrange them daily, so that no two shall walk twice abreast.
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Sacituzumab Govitecan in Metastatic Triple-Negative Breast Cancer
New England Journal of Medicine, 2021Aditya Bardia +2 more
exaly