Search Results - "BENNETT, E. F"

Super-simple Steiner pentagon systems by Abel, R.J.R., Bennett, F.E.

“…A Steiner pentagon system of order v ( SPS ( v ) ) is said to be super-simple if its underlying ( v , 5 , 2 ) -BIBD is super-simple; that is, any two blocks of…”
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Recent progress on the existence of perfect Mendelsohn designs by Bennett, F.E.

“…A necessary condition for the existence of a ( v, k, λ)-PMD is λv(v−1)≡0 ( mod k) . For k=3, 4 , and 5, some fairly conclusive results have already been…”
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Perfect Mendelsohn designs with block size six by Abel, R.J.R., Bennett, F.E., Zhang, H.

“…A necessary condition for the existence of a ( v, k, λ)-perfect Mendelsohn design is λv( v−1)≡0 (mod k). For k=6 and λ=1, this condition gives v≡0,1,3 or 4…”
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Super-Simple Twofold Steiner Pentagon Systems by Abel, R. J. R., Bennett, F. E.

“…A twofold pentagon system of order v is a decomposition of the complete undirected 2-multigraph 2 K v into pentagons. A twofold Steiner pentagon system of…”
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Resolvable perfect Mendelsohn designs with block size five by Abel, R.J.R., Bennett, F.E., Ge, G.

“…A necessary condition for the existence of a resolvable (v,5,1)-perfect Mendelsohn design is v≡0 ( mod 5) . This condition is shown to be sufficient for v⩾215,…”
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Almost resolvable perfect Mendelsohn designs with block size five by Abel, R.J.R., Bennett, F.E., Ge, G.

“…A necessary condition for the existence of an almost resolvable ( v,5,1)-perfect Mendelsohn design is v≡1 ( mod 5) . This condition is shown to be sufficient…”
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Super-simple, pan-orientable and pan-decomposable GDDs with block size 4 by Abel, R.J.R., Bennett, F.E.

“…In this paper we study ( 4 , 2 μ ) -GDDs of type g n possessing both the pan-decomposable property introduced by Granville, Moisiadis, Rees, On complementary…”
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Existence of Steiner seven-cycle systems by Abel, R.J.R., Bennett, F.E., Ge, G., Zhu, L.

“…A Steiner k-cycle system of order v is a pair (X,C), where C is a collection of k-cycles of K v based on a v-set X such that for any integer r, 1⩽r⩽k/2 , and…”
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A brief survey of perfect Mendelsohn packing and covering designs by Bennett, F.E.

“…A ( v, k, λ)-perfect Mendelsohn packing (covering) design is a pair (X, A) where X is a v-set of points and A is a collection of cyclically ordered k-subsets…”
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Holey Steiner pentagon systems and related designs by Bennett, F.E., Ge, G., Zhang, H., Zhu, L.

“…Certain types of holey Steiner pentagon systems (HSPSs) are investigated. New HSPSs are found, which improve an earlier existence result. These HSPSs are used…”
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Existence of directedwhist tournaments with the three person property 3PDWh(v) by BENNETT, F. E, GENNIAN GE

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Minimum matrix representation of Sperner systems by Bennett, F.E., Wu, L.

“…Let X be an n-element set and2 X be the family of subsets of x. IfK⊂ 2 x such that for any K 1, K 2 εK, k 1 ≠ K 2 implies K 1 ≠ K 2 thenKis called a Sperner…”
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Super-simple, Pan-orientable, and Pan-decomposable BIBDs with Block Size 4 and Related Structures by Abel, R. J. R., Bennett, F. E., Grüttmüller, M.

“…Let v , k , and  μ be positive integers. A tournament T of order k , briefly k -tournament, is a directed graph on k vertices in which there is exactly one…”
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Quintessential PBDs and PBDs with prime power block sizes ≥ 8 by Abel, R. J. R., Bennett, F. E.

“…In this paper, we look at the existence of (v K) pairwise balanced designs (PBDs) for a few sets K of prime powers ≥ 8 and also for a number of subsets K of…”
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The existence of perfect Mendelsohn designs with block size 7 by Abel, R.J.R., Bennett, F.E.

“…Necessary conditions for existence of a ( v,k,λ) perfect Mendelsohn design (or PMD) are v ⩾ k and λv( v − 1) ≡ 0 mod k. When k = 7, this condition is satisfied…”
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Steiner pentagon covering designs by Abel, R.J.R., Bennett, F.E., Zhang, H., Zhu, L.

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Holey Steiner pentagon systems by Abel, R. J. R., Bennett, F. E., Zhang, H.

“…In this article, it is shown that the necessary conditions for the existence of a holey Steiner pentagon system (HSPS) of type hn are also sufficient, except…”
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The spectrum of HSOLSSOM( hn) where h is even by Bennett, F.E., Zhu, L.

“…In this paper, we describe a generalized product construction and a construction using Steiner pentagon systems to obtain holey self-orthogonal Latin squares…”
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Quintessential pairwise balanced designs by Bennett, Frank E., Colbourn, Charles J., Mullin, Ronald C.

“…The existence of pairwise balanced designs with block sizes from a set K is studied. The spectrum of orders for which such PBDs exist is determined when {5}⊂…”
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Packings and coverings of the complete directed multigraph with 3- and 4-circuits by Bennett, F.E., Yin, J.

“…Let λDK v denote the complete directed multigraph with v vertices, where any two distinct vertices x and y are joined by λ arcs ( x, y) and λ arcs ( y, x). By…”
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