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Dec
16
answered A proposition on cyclic group
Dec
3
comment Fixed point of fatness
@PietroMajer: They are. The critical situation is a rhombus with angles $\pi/3$ and $2\pi/3$; then it is 2-fat, and it can be cut into two isosceles triangles, which are also 2-fat.
Nov
30
comment Existence of solution for this set of polynomial equations
In your second system, shouldn't there be $(1-t_i)^k$ instead of $(t_i)^k$?
Nov
27
answered n-cube connectivity problem
Nov
26
revised A question about generalized Dyck words
added 14 characters in body
Nov
26
revised A question about generalized Dyck words
added 9 characters in body
Nov
26
answered A question about generalized Dyck words
Nov
24
revised Distribution of the permanent modulo $p$
added 6 characters in body
Nov
24
answered Isomorphic Hadwiger graphs
Nov
21
comment “Nyldon words”: understanding a class of words factorizing the free monoid increasingly
@Wolfgang: But a Nyldon word may start with a square, as 1011010 does. Perhaps, we should excludr not all squares?
Nov
21
comment “Nyldon words”: understanding a class of words factorizing the free monoid increasingly
I do not see that Nyldon words are pattern avoiding. E.g., $101101010\dots10$ is a Nyldon word.
Nov
20
awarded  Enlightened
Nov
20
awarded  Nice Answer
Nov
18
comment “Nyldon words”: understanding a class of words factorizing the free monoid increasingly
Thanks! Now it's much easier to falsify the conjectures;)
Nov
18
comment Is there a bounded sequence of points in the plane with pairwise distances at least $1/\sqrt{|i-j|}$?
@Douglas Zare: Yes, it seems that this modification works; the proof I can imagine looks similar to what's above.
Nov
18
comment Is there a bounded sequence of points in the plane with pairwise distances at least $1/\sqrt{|i-j|}$?
@Yaakov: No; it is close to my earlier (unsuccessful) attempt. Check what happens with the numbers $i=\overline{011\dots100}$ and $j=\overline{100\dots011}$ which differ by 7. My (hopefully working) recent approach is different --- see my first comment.
Nov
18
comment Is there a bounded sequence of points in the plane with pairwise distances at least $1/\sqrt{|i-j|}$?
In fact, in the second part we construct the sequence of integer points $(m(i),n(i))$ such that for all $i>j$ either $0<|m(i)-m(j)|<4\sqrt{i-j}$ or $0<|n(i)-n(j)|<4\sqrt{i-j}$.
Nov
18
comment “Nyldon words”: understanding a class of words factorizing the free monoid increasingly
Darij, wouldn't it be better to put into `Exp. data' the corresponding sets of Lyndon words? Just for comparison...
Nov
18
answered Is there a bounded sequence of points in the plane with pairwise distances at least $1/\sqrt{|i-j|}$?
Nov
18
comment Is there a bounded sequence of points in the plane with pairwise distances at least $1/\sqrt{|i-j|}$?
@joro: You cannot get an example lying on a circle (or on any rectifiable curve), because the smallest pairwise distance between $n$ points on such curve is $O(1/n)$.