Let Fin(v) = {(s, t) : ∃ a pair of (K_4−e)-designs of order v intersecting in s blocks and 2s+t triangles}. Let Adm(v) = {(s, t) : s+t ≤ b_v , s ∈ J(v), 2s+t ∈ J_T (v)}\{(bv−3, 1)}, where J(v) (or J_T (v)) denotes the set of positive integers s (or t) such that there exists a pair of (K_4−e)-designs of order v intersecting in s blocks (or t triangles), and b_v = v(v−1)/10. It is established that Fin(v) = Adm(v) for any integer v ≡ 0, 1 (mod 5), v ≥ 6 and v≠ 10, 11.
The fine triangle intersection problem for (K_4-e)-designs
LO FARO, Giovanni;TRIPODI, Antoinette
2011-01-01
Abstract
Let Fin(v) = {(s, t) : ∃ a pair of (K_4−e)-designs of order v intersecting in s blocks and 2s+t triangles}. Let Adm(v) = {(s, t) : s+t ≤ b_v , s ∈ J(v), 2s+t ∈ J_T (v)}\{(bv−3, 1)}, where J(v) (or J_T (v)) denotes the set of positive integers s (or t) such that there exists a pair of (K_4−e)-designs of order v intersecting in s blocks (or t triangles), and b_v = v(v−1)/10. It is established that Fin(v) = Adm(v) for any integer v ≡ 0, 1 (mod 5), v ≥ 6 and v≠ 10, 11.File in questo prodotto:
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