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ON STEINER LOOPS AND POWER ASSOCIATIVITY 217

by Palaniappan Kannappan
"... Abstract. In this paper we investiagte Steiner loops introduced by N.S. Mendel-sohn [Aeq. Math. 6 (1991), 228–230] and provide six (seven) equivalent iden-tities to characterize it. We also prove the power associativity of Bol loops by using closure (Hexagonal) conditions. 1. Steiner loops In [9] Me ..."
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] Mendelsohn has defined the concept of a generalized triple system as follows. Let S be a set of ν elements. Let T be a collection of b subsets of S, each of which contains three elements arranged cyclically, and such that any ordered pair of elements of S appears in exactly a cyclic triplet (note the cyclic

Antipodal Triple Systems

by P. B. Gibbons, E. Mendelsohn, H. Shen - AUSTRALASIAN JOURNAL OF COMBINATORICS 9(1994). NN. B7-1&;1 , 1994
"... An antipodal triple system of order v is a triple (V, B, 1), where 1 V 1 = v, B is a set of cyclically oriented 3-subsets of V, and f: V-+ V is an involution with one fixed point such that: (i) (V, B U f(B)) is a Mendelsohn triple system. Oi) B n f(B) = 0. (iii) f is an isomorphism between the Stei ..."
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An antipodal triple system of order v is a triple (V, B, 1), where 1 V 1 = v, B is a set of cyclically oriented 3-subsets of V, and f: V-+ V is an involution with one fixed point such that: (i) (V, B U f(B)) is a Mendelsohn triple system. Oi) B n f(B) = 0. (iii) f is an isomorphism between

Construction of extended Steiner systems for information retrieval

by Eun-young Park, Ian Blake - Revista Matemática Complutense , 2008
"... A multiset batch code is a variation of information retrieval where a t-multiset of items can be retrieved by reading at most one bit from each server. We study a problem at the other end of the spectrum, namely that of retrieving a t-multiset of items by accessing exactly one server. Our solution t ..."
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to the problem is a combinatorial notion called an extended Steiner system, which was first studied by Johnson and Mendelsohn [11]. An extended Steiner system ES(t, k, v) is a collection of k-multisets (thus, allowing repetition of elements in a block) of a v-set such that every t-multiset belongs to exactly one
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