Interchangeable variables and values

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Some special cases • Interchangeable values but not variables • i.e. a=n • Ordering signatures = value precedence • (X1=k,X2=k, ...) ≥lex (X1=k+1,X2=k+1, ...) • Consider k=3, and (X1,..,X6)=(1,1,2,1,3,4)
Some special cases • All variables and values are interchangeable • i.e. a=b=1 • Ordering signatures = “decreasing sequence” • X1 ≤ X2 ≤ .. ≤ Xn • |{ i | Xi=k}| ≥ |{ i | Xi=k+1}| for all k • Consider 1,1,1,2,2,3,4 and 1,1,1,2,2,3,5 or 1,1,2,2,2,3,4
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 and 18: • • Variables partition into tw
Page 19: Ordering signatures • Equivalent
Page 23 and 24: Conclusions • Symmetry occurs in

Interchangeable variables and values

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