bio | website | |
---|---|---|
location | Moscow | |
age | 37 | |
visits | member for | 3 years, 3 months |
seen | yesterday | |
stats | profile views | 1,296 |
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 $O(1/n)$. |