In this paper the triangle intersection problem for S(2, 4, v) designs is investigated. Let t(v) = v(v - 1)/3 and I(v)_T = {0, 1, ..., t(v) - 30} ∪ ∪ {t(v) - 27, t(v) - 24, t(v) - 18, t(v)}. Let J(v)_T = {s| there exist two S(2, 4, v) designs with s common triangles}. We show that for any positive integer v ≡ 1, 4 (mod 12), J(v)_(T) = I(v)_T when v≥ 121, and I(v)_T {t(v) - 33} ⊆ J(v)_(T) ⊆I(v)_T when 49 ≤ v ≤ 112.
The triangle intersection problem for S(2, 4, v) designs
LO FARO, Giovanni
2010-01-01
Abstract
In this paper the triangle intersection problem for S(2, 4, v) designs is investigated. Let t(v) = v(v - 1)/3 and I(v)_T = {0, 1, ..., t(v) - 30} ∪ ∪ {t(v) - 27, t(v) - 24, t(v) - 18, t(v)}. Let J(v)_T = {s| there exist two S(2, 4, v) designs with s common triangles}. We show that for any positive integer v ≡ 1, 4 (mod 12), J(v)_(T) = I(v)_T when v≥ 121, and I(v)_T {t(v) - 33} ⊆ J(v)_(T) ⊆I(v)_T when 49 ≤ v ≤ 112.File in questo prodotto:
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