An Open Problem in Embedding
Copyright policy )An Open Problem in Embedding
We propose and study the problem of finding the smallest nonnegative integer s such that a GDD ( m , n , 3 ; 0 , λ ) can be embedded into a BIBD ( m n + s , 3 , λ ) . We find the values of s for all cases except for the case where n ≡ 5 ( mod 6 ) and m ≡ 1 , 3 ( mod 6 ) and m ≥ 3 , which remains as an open problem.
\(k\)-Dyck paths, Triple systems, generating functions, Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.), Exact enumeration problems, generating functions, bijections, Combinatorial aspects of block designs
\(k\)-Dyck paths, Triple systems, generating functions, Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.), Exact enumeration problems, generating functions, bijections, Combinatorial aspects of block designs
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