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A new construction for μ-way Steiner trades.
- Source :
- Communications in Combinatorics & Optimization; 2024, Vol. 9 Issue 2, p329-338, 10p
- Publication Year :
- 2024
-
Abstract
- A μ-way (v,k,t) trade T of volume m consists of μ pairwise disjoint collections Ti,...,Tμ, each of m blocks of size k such that for every t-subset of a v-set V, the number of blocks containing this t-subset is the same in each Ti for 1 ≤ i ≤ μ. If any t-subset of the v-set V occurs at most once in each Ti for 1 ≤ i ≤ μ, then T is called a μ-way (v, k, t) Steiner trade. In 2016, it was proved that there exists a 3-way (v, k, 2) Steiner trade of volume m when 12(k - 1) ≤ m for each k. Here we improve the lower bound to 8(k - 1) for even k, by using a recursive construction. [ABSTRACT FROM AUTHOR]
- Subjects :
- SUBSET selection
MATHEMATICAL bounds
RECURSIVE functions
COMBINATORICS
PERMUTATIONS
Subjects
Details
- Language :
- English
- ISSN :
- 25382128
- Volume :
- 9
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Communications in Combinatorics & Optimization
- Publication Type :
- Academic Journal
- Accession number :
- 175588561
- Full Text :
- https://doi.org/10.22049/cco.2023.27862.1373