Interchangeable variables and values

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Symmetry • Symmetry is bijection, σ on assignments that preserves solutions/constraints • • • In armies of queens problem, swap colours! X[1,3]=white queen, X[6,2] =black queen .. X[1,3]=black queen, X[6,2] =white queen ..
Types of symmetry • Which part of the assignment does the bijection act upon? • Variable symmetry • Value symmetry • Variable/value symmetry
Page 1: Interchangeable variables and value
Page 5 and 6: Adding constraints • Same method
Page 7 and 8: Interchangeable variables and value
Page 9 and 10: Signature of an assignment • Can
Page 11 and 12: Signature of an assignment • Supp
Page 13 and 14: Signature of an assignment • Sign
Page 15 and 16: Ordering signatures • To break al
Page 17 and 18: • • Variables partition into tw
Page 19 and 20: Ordering signatures • Equivalent
Page 21 and 22: Some special cases • All variable
Page 23 and 24: Conclusions • Symmetry occurs in

Interchangeable variables and values

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