Interchangeable variables and values

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• • 30 proper colourings • • An example But only 3 if we break symmetry X1,..X5 is 1,1,2,2,2, or 1,1,2,2,3 or 1,2,3,3,3 Some of the colourings eliminated by ordering signatures • 2,1,3,3,3 and 1,1,3,3,3 and 1,1,2,3,3 X1 X2 X3 X4 X5
Ordering signatures • Equivalent to the exponential number of LEX LEADER constraints • But only requires a polynomial number of constraints • Channel into a count on occurrences of values within each equivalence class • O[i,k] = |{ j | X[j]=k & p(i)≤j
Page 1 and 2: Interchangeable variables and value
Page 3 and 4: Types of symmetry • Which part of
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: • • Variables partition into tw
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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