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jaanos / sage-drg

A Sage package for checking feasibility of distance-regular graph and association scheme parameter sets
MIT License
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unfeasibility of existing graph #2

Closed Ivo-Maffei closed 4 years ago

Ivo-Maffei commented 4 years ago

I can construct a distance regular graph with intersection array [64,42,1,1,21,64]. However, checking the feasibility of those parameters with drg yields an InfeasibleError. The error message is no corresponding 2-design: nonexistence by BCN, Prop. 1.10.5. The said proposition is not violated as we have $r = 3$ , $\mu = 21$ and so the equation $kX^2+(-1)^{(r-1)/2} rY^2 = Z^2$ boils down to $64X^2-3Y^2 = Z^2$ which has solutions $X=1, Y=0, Z=8$.

jaanos commented 4 years ago

Thanks for noticing this, it should work correctly now.

The previous code missed certain examples when X = 0 or Y = 0 (note that Z = 0 is not possible) - of course, such examples arise when either of the coefficients is a square. Note that for the contrary case, only a feasibility condition is checked (namely, that each coefficient is a square residue modulo the other) - I am not sure that this is actually sufficient for the existence of a solution. If you have any idea how to efficiently perform such a test, please let me know.