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Apr
23 |
comment |
origin of analogy “primes as the atoms of number theory/ arithmetic”
ps oops that meant to say 20th century physics in the question. ofc 20th century physics highly revised the idea/ concept of the atom at the turn of the century with QM physics etc. note: even the greeks/ Leucippus/ Democritus over 2 millenia ago posited existence of physical atoms but afaik the idea of relating primes to atoms did not originate with them, it appears only in "modern" thought. also, am looking for any earlier refs by experts than the Sautoy one if its not a long list and it may be difficult to definitively isolate the earliest ref. |
Apr
23 |
asked | origin of analogy “primes as the atoms of number theory/ arithmetic” |
Nov
4 |
awarded | Civic Duty |
Sep
11 |
awarded | Necromancer |
Jul
31 |
comment |
Partitioning graph for Graph Isomorphism
@Brendan can you cite something that would point to "the hardest graphs for the isomorphism problem"? arent they thought to be regular? thx! |
Jul
9 |
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Complexity of reordering a matrix which consists independent sub matrices
extended discussion in chat |
Jun
29 |
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A circulant coin weighing problem
not an expert in this but looking further. this paper "Münchhausen Matrices" / Brand also studies a variant of the coin weighing problem and says p3 there are different "weighing matrices" going back to a definition at least to 1946 [14] for "Hotellings weighing problem". is the wikipedia entry referring to the latter? |
Jun
29 |
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A circulant coin weighing problem
@Anush did you look it up on wikipedia, weighing matrices? |
Jun
19 |
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Probability of many overlapping zero inner products on a circle
some basic ideas are not being defined. what is i th rotation of v ? etc. if not phrased in some std ways & not linked into any other std study (what field is this from? motivation? etc) then maybe a short intro/ writeup elsewhere would help |
Mar
15 |
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Collatz property implying infinite “fall below” trajectories, is it known?
thx for further attn however afaik collatz implies the "fall below" property highlighted in the question for an infinite # of cases but not vice versa as your answer seems to assert. but the strict formulation of the property is more found in the followup comments. suggest/ encourage further discussion/ clarification in number theory chat |
Dec
14 |
comment |
Invariants that might determine graph up to isomorphism
re HS comment, it would be good if the author of the paper updates it to state the error and extract anything else useable from the framework. otherwise there may be further questions |
Oct
22 |
awarded | Nice Answer |
Sep
24 |
awarded | Autobiographer |
Aug
27 |
awarded | Informed |
Aug
26 |
comment |
Do the base 3 digits of $2^n$ avoid the digit 2 infinitely often — what is the status of this problem?
Tao (end of blog post) cites some refs & draws some analogy to the collatz conjecture. apparently Erdos conjectured "2" always appears in the base-3 expansion for all $i>8$ |
Aug
21 |
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Collatz property implying infinite “fall below” trajectories, is it known?
Aeryks formulation is what is intended, thx for that (mea culpa for not initially rigorously stating it). have worked with "backwards" algorithms like what AlexR refers to but dont know what mathematical form the sets take, have to think about that more, dont see how to derive the above property that way. (note property is implied by Collatz conjecture.) |
Aug
21 |
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Collatz property implying infinite “fall below” trajectories, is it known?
the "fall below" property is interrelated but not exactly the same as the "terminates at 1" property. the conjecture is also true iff all trajectories "fall below". but a "fall below" property of a trajectory does not nec(?) guarantee it terminates at 1. (by induction) a "fall below" trajectory does terminate at 1 if all trajectories starting below it also have the "fall below" property. here "full trajectory" means a trajectory ending at 1. |
Aug
20 |
asked | Collatz property implying infinite “fall below” trajectories, is it known? |
Aug
14 |
comment |
Examples of unexpected mathematical images
also see eg Phase Plots of Complex Functions: a Journey in Illustration / Wegert, used to visualize the Riemann zeta fn & related ones |
Aug
11 |
answered | Examples of unexpected mathematical images |