Papers › Some exact values of the inducibility and statistics constants for hypercubes
Some exact values of the inducibility and statistics constants for hypercubes
Levente Bodnár, Oleg Pikhurko
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We consider two types of problems: maximising, over subsets S⊆{0,1}ⁿ, the density of d-subcubes C in the n-hypercube graph that span a subgraph such that S∩C is i) isomorphic to the given configuration H⊆{0,1}ᵈ (the inducibility problem), or ii) has the given size s (the statistics problem). Using flag algebras, we determine the limit of this density as n→∞ for 5 new configurations H⊆{0,1}³ and for 3 new pairs (d,s), namely for (3,2), (4,2) and (4,4). Interestingly, the lower bounds in the last three cases come from blowups of small Hamming codes.
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