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[5]: 127 [9] This is similar to shroud, but it does not deny the player (or their allies) the ability to target their own hexproof permanents. Cards that previously had or granted this ability were updated via rules errata to have hexproof with the release of the Commander decks.
The permanents corresponding to the smallest projective planes have been calculated. For n = 2, 3, and 4 the values are 24, 3852 and 18,534,400 respectively. [13] Let Z be the incidence matrix of the projective plane with n = 2, the Fano plane. Remarkably, perm(Z) = 24 = |det (Z)|, the absolute value of the determinant of Z.
In computational complexity theory, a theorem of Valiant states that computing permanents is #P-hard, and even #P-complete for matrices in which all entries are 0 or 1 Valiant (1979). This puts the computation of the permanent in a class of problems believed to be even more difficult to compute than NP .
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The clause component is a weighted, directed graph with 7 nodes with edges weighted and nodes arranged to yield the properties specified above, and is given in Appendix A of Ben-Dor and Halevi (1993). Note that the internal edges here have weights drawn from the set {,,,,}; not all edges have 0–1 weights.
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