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1d
comment Can all unit-distance graphs have their vertices at algebraic integers?
Thanks! The link to the first one was in my answer, but I did not know about the second.
2d
awarded  Nice Answer
2d
comment Can all unit-distance graphs have their vertices at algebraic integers?
@David: Do you know the exact reference?
Jan
26
revised Can all unit-distance graphs have their vertices at algebraic integers?
Remark has been expanded
Jan
26
answered Can all unit-distance graphs have their vertices at algebraic integers?
Jan
26
comment Can all unit-distance graphs have their vertices at algebraic integers?
@Dima: Not much difference. A hexagonal lattice maps to $K_3$...
Jan
26
comment Irreducibility of a polynomial
Sorry, I do not understand why this question is closed.
Jan
26
comment Can all unit-distance graphs have their vertices at algebraic integers?
@Dima: I just meant that two such roots with a zero form a triangle. So you may consider homomorphisms to a 6-wheel (which pass to $K_3$ though).
Jan
26
comment Can all unit-distance graphs have their vertices at algebraic integers?
@Dima: The 6th degree roots of unity are algebraic integers.
Jan
23
comment Is mean width a Dehn invariant?
I do not think $W$ is invariant under scissor congruence. Compare the orders of magnitude of mean widths of $1\times 1\times N^3$ amd $N\times N\times N$ boxes.
Jan
21
answered Density of tuples of conjugate algebraic numbers
Jan
13
comment What is the smallest 4-chromatic graph of girth 5?
Since $\delta\geq 3$, we may estimate $\Delta$ better. Take any vertex of degree $\Delta$; all its $\Delta$ neighbors, as well as their $\geq (\delta-1)\Delta$ other neighbors are distinct (due to the girth condition), so there are at least $1+\Delta\delta$ vertices at all. Thus, if $\Delta\geq 7$ then there are at least 22 vertices, and we may assume $\Delta\leq 6$.
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