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Jul
8
comment Sum set fixpoint, how many iterations?
Remark for the interested reader, if the lemma holds for sets S_i, it would also hold for integer intervals I_i, since an interval is only a special case of a set.
Jul
8
comment Sum set fixpoint, how many iterations?
Maybe an alternate proof could use monotonicity of Minkowsky sum, i.e. A subset B implies A + C subset B + C. Not sure. But I am already happy to see the question settled.
Jul
8
comment Sum set fixpoint, how many iterations?
Ok I guess the argument runs along the following for a x_i in S^0_i \ S^1_i there was anyway no (x_j)_j<>i, so when "deleting" x_i from S^0_i it will not reduce any of the S^0_j for j<>i.
Jul
8
comment Sum set fixpoint, how many iterations?
Was also hypothesizing once that the fixpoint is reached after maximal 1 iteration. Did not yet have time to produce a counter example. What is exactly the argument behind S^2_i = S^1_i in the general case?
Jul
6
revised Sum set fixpoint, how many iterations?
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Jul
6
comment Sum set fixpoint, how many iterations?
It looks the problem can be reduced to y_1 + .. + y_n + b = 0, by using y_i = a_i * x_i. We can also find sets T_i with y_i in T_i, by T_i = a_i * S_i. And then ask for fixpoint of (T_1,..,T_n).
Jul
4
comment Sum set fixpoint, how many iterations?
In the case of n=2 a simple geometric argument shows that l=<1 is sufficient. Right? But for n>2, is there also a fixed bound?
Jul
4
comment Sum set fixpoint, how many iterations?
I thought it is the other way around by construction of the mapping, i.e. S_i^k+1 subset S_i^k. But otherwise I agree, this is the worst case. But is it possible that it happens?
Jul
4
revised Sum set fixpoint, how many iterations?
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Jul
4
revised Sum set fixpoint, how many iterations?
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Jul
4
revised Sum set fixpoint, how many iterations?
edited tags
Jul
4
asked Sum set fixpoint, how many iterations?
Jun
19
accepted Sum set estimates for cofinite integer sets
Jun
19
revised Sum set estimates for cofinite integer sets
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Jun
19
revised Sum set estimates for cofinite integer sets
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Jun
19
asked Sum set estimates for cofinite integer sets
Jun
16
accepted Minimal bivariate diophantine equation solution space
Jun
16
asked Minimal bivariate diophantine equation solution space
Mar
19
revised Is there an intuitionistic proof of $\lnot p(a) \rightarrow p(b) \vdash \exists x p(x)$, what would Herbrand's Theorem say?
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Mar
18
revised Contradiction Theorem
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