On the 3-way (v,k,2) Steiner trades
نویسندگان
چکیده
منابع مشابه
On the existence of 3-way k-homogeneous Latin trades
A μ-way Latin trade of volume s is a collection of μ partial Latin squares T1, T2, . . . , Tμ, containing exactly the same s filled cells, such that if cell (i, j) is filled, it contains a different entry in each of the μ partial Latin squares, and such that row i in each of the μ partial Latin squares contains, set-wise, the same symbols and column j, likewise. It is called μ–way k–homogeneous...
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A μ-way k-homogeneous Latin trade was defined by Bagheri Gh, Donovan, Mahmoodian (2012), where the existence of 3-way k-homogeneous Latin trades was specifically investigated. We investigate the existence of a certain class of μ-way k-homogeneous Latin trades with an idempotent like property. We present a number of constructions for μ-way k-homogeneous Latin trades with this property, and show ...
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The main result of this paper is the determination of all pairwise nonisomorphic trade sets of volume at most 10 which can appear in Steiner triple systems. We also enumerate partial Steiner triple systems having at most 10 blocks as well as configurations with no points of degree 1 and tradeable configurations having at most 12 blocks.
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In this note we investigate the minimum possible volumes for strong Steiner trades (SST). We prove that a (v, q + 1,2) SST must have at least q2 blocks if q is even and q2 + q blocks if q is odd. We construct a (v, q+ 1, 2) SST of volume q2 for every q a power of two, and a (v, q+ 1, 2) SST of volume q2 + q, for every q such that q + 1 is a power of two. A construction of (q2 + q + 1, q + 1,2) ...
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In this paper we focus on the representation of Steiner trades of volume less than or equal to nine and identify those for which the associated partial latin square can be decomposed into six disjoint latin interchanges. 1 Background information In any combinatorial configuration it is possible to identify a subset which uniquely determines the structure of the configuration and in some cases i...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2016
ISSN: 0012-365X
DOI: 10.1016/j.disc.2016.06.006