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Feb
17 |
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Grover's Quantum Search Algorithm
You might be interested in this question on cstheory for a more thorough discussion which decomposes $U$ into gates of finite width. |
Feb
12 |
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Separations between notions of rank for modules over commutative (semi-)rings with no zero divisors.
I don't need the three definitions to be consistent, I am happy with them being different, I just want to see if I can bound the gap that separates them by something reasonable. Your examples in P1 shows that for my initial flawed definition of linear-independence, I can't bound it at all (better than 1 versus max of $n$, $m$) if I allow arbitrarily large coefficients, and if I count the number of bits to represent coefficients, I still can't hope for a small gap. |
Feb
12 |
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Separations between notions of rank for modules over commutative (semi-)rings with no zero divisors.
Yes, the ring is a module, but I was hoping for examples that really use the module-ness and not just the ring-ness. I know, I'm impossible to please! Sorry. |
Feb
12 |
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Separations between notions of rank for modules over commutative (semi-)rings with no zero divisors.
I modified the definition of linear independence I use to better approximate the one you give in paragraph 2 but that will still work for what I need on semi-rings. Thanks for your counter-example in helping clarify my answer, I will give a +1 but won't accept in hopes of other answers. Sorry for the "chase the definition" edits, I am trying to formulate this precisely in my mind since it comes from specific applications. |
Feb
12 |
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Separations between notions of rank for modules over commutative (semi-)rings with no zero divisors.
Your paragraph 1 example is very much like the one I tried to rule out by excluding zero-divisors, and can be generalized to give arbitrary separation by, for instance, taking the first $n$-primes with product $N = p_1\cdot...\cdot p_n$ and then taking a row matrix $M = [a_1 , ... , a_n]$ where $a_j = P/p_j$. |
Feb
12 |
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Separations between notions of rank for modules over commutative (semi-)rings with no zero divisors.
Thanks for the example in paragraph 1, it still rides in on just the ring, so I need to think about my question more. Paragraph 2: I specifically don't want to use that definition of algebraic dependence (see note 1) because in semi-rings we don't have minus and so it isn't clear that it is more general but just different (same with rings with zero-divisors). Paragraph 3: I am not looking for other ranks, but specifically the ones I defined in the question (this comes from an application in CS); is there a way in which the definition of rank you give here relates to the two I list? |
Feb
12 |
asked | Separations between notions of rank for modules over commutative (semi-)rings with no zero divisors. |
Feb
8 |
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Jan
29 |
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Minimize the length of intersection of the set of intervals
This question was cross-posted to cstheory. |
Jan
27 |
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Demonstrating that rigour is important
I hope I'm not flogging a dead horse, but there is a great discussion on cstheory that was spawned by this thread and fits with @gowers 'further addition' section. In particular, it is a list of cstheory results where the rigorous demonstration of an 'obviously true' statement resulted in interesting insights. |
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25 |
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Aug
25 |
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how to use arxiv?
there is some good advice here: cstheory.stackexchange.com/q/7574/1037 |
Aug
25 |
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how to use arxiv?
I asked a similar question on putting up things that don't go to journal of the theoretical CompSci version of MO: cstheory.stackexchange.com/q/7574/1037 and the consensus seemed to be that its fine as long as its not something you plan to extend and make into a future article (to avoid redundancy and confusion). |
Aug
9 |
awarded | Yearling |
Jul
15 |
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Lower bounding the maximum size of sets in a set family with union promise
Added a more formal statement, hopefully it is clear. Paseman's more informal restatement also works. |