On the existence of d-homogeneous 3-way Steiner trades
| Main Author: | H. Amjadi and N. Soltankhah |
|---|---|
| Format: | info publication-preprint |
| Terbitan: |
, 2019
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| Subjects: | |
| Online Access: |
https://zenodo.org/record/3334140 |
Daftar Isi:
- A μ-way (v; k; t) trade T = fT1; T2; :::; Tμg of volume m consists of μ disjoint collections T1; T2; :::; Tμ, each of m blocks of size k, such that for every t-subset of v-set V the number of blocks containing this t-subset is the same in each Ti (for 1 ≤ i ≤ μ). A μ-way (v; k; t) trade is called μ-way (v; k; t) Steiner trade if any t-subset of found(T) occurs at most once in T1 (Tj; j ≥ 2). A μ-way (v; k; t) trade is called d-homogeneous if each element of V occurs in precisely d blocks of T1 (Tj; j ≥ 2). In this paper we characterize the 3-way 3-homogeneous (v; 3; 2) Steiner trades of volume v. Also we show how to construct a 3-way d-homogeneous (v; 3; 2) Steiner trade for d 2 f4; 5; 6g, except for seven small values of v.