Seva
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Registered User
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1d |
awarded | ● Nice Question |
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May 17 |
comment |
Fano plane drawings: embedding PG(2,2) into the real plane Hm-m-m... I'd say you do use this - at least, for the real case. Let $A,B,C,O,A',B',C'$ be as in your comment. How many of the points $A',B',C'$ lie on the edges of the triangle $ABC$? An odd number, on the one hand (they are points of intersection of $OA$, $OB$, $OB$ with the edges), and an even number, on the other hand (they are points of intersection of the straight line through $A',B'$ and $C'$ with the edges) - a contradiction. |
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May 16 |
comment |
Fano plane drawings: embedding PG(2,2) into the real plane @Noam: I see, the basic idea is that (1) any line not passing thorough a vertex of a triangle intersects an even number of its edges, while (2) for any triangle $ABC$, and any point $O$ not on its boundary, the three lines $OA$, $OB$, and $OC$ intersect an odd number of the edges. |
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May 15 |
comment |
Fano plane drawings: embedding PG(2,2) into the real plane Seems it does - very nice! |
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May 14 |
asked | Fano plane drawings: embedding PG(2,2) into the real plane |
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May 10 |
comment |
Bounding number of solutions to an equation: It may be useful to rewrite your equation as $au^2-bv^2=d$, where $u=2x-1$, $v=2y-1$, and $d=a+c-b$, and then factor the left-hand side. |
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Apr 19 |
accepted | Additive Combinatorics - reference request |
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Apr 19 |
comment |
Additive Combinatorics - reference request Not that I could recall it, at least... |
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Apr 19 |
answered | Additive Combinatorics - reference request |
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Apr 15 |
accepted | Perimeter/Neighborhood of a graph on grid |
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Apr 14 |
revised |
Perimeter/Neighborhood of a graph on grid Tags edited |
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Apr 14 |
answered | Perimeter/Neighborhood of a graph on grid |
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Mar 26 |
comment |
More expanders? It is my understanding, by the way, that the situation changes significantly, and the argument does not work any longer, if one fixes two non-zero elements $e_1$ and $e_2$, and has every $z$ adjacent to both $z+e_1$ and $z+e_2$ (in addition to $g^{\pm1}z$)? |
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Mar 25 |
revised |
More expanders? added 32 characters in body; deleted 3 characters in body |
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Mar 25 |
comment |
More expanders? The argument for the second graph is really nice, thanks! |
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Mar 22 |
comment |
More expanders? The union of, say, three cliques with a bridge between any pair of them has a very small diameter, but is not an expander? |
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Mar 22 |
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More expanders? @Noam: sorry, do not get it. First, any (non-zero) field element is actually just a power of $g$. Second, I do not see why the diameter being logarithmic implies that the graph is an expander. (To my understanding, it does not - am I missing something? Could you expand? :-) ) |
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Mar 22 |
comment |
More expanders? @Freddie Manners: concerning the first graph I mentioned - you are absolutely right, pretty stupid of me not to notice this myself. Concerning the second graph - I still don't see any obvious reason for it not to be an expander. |
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Mar 22 |
asked | More expanders? |
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Mar 20 |
awarded | ● Notable Question |
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Mar 17 |
comment |
An expander (?) graph Sorry for being unable to accept both answers... Thanks, anyway! |
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Mar 16 |
asked | An expander (?) graph |
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Mar 6 |
answered | Formal writing: numbers under 10 |
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Feb 18 |
comment |
nonnegative Fourier Transform What do you call "the other inequality" and where your question originates from? |
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Feb 11 |
comment |
A sum involving mod(n) arithmetic The sum of WHAT, and what exactly is your question? |
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Feb 11 |
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Minimum number of solutions in a system of equalities and non-equalities How about fixing the typo(s) and motivating your question to convince the community that this is not a homework problem? |
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Feb 10 |
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How large can a non-sumset be? @J.H.S.: the link, I believe, is correct, but there seems to be some temporary problem with the Tel Aviv university server. Anyway, the paper is most certainly by Alon, entitled "Large sets in finite fields are sumsets" and published in the J. Number Theory 126 (1) (2007), pp. 110–118. |
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Feb 7 |
comment |
Bounds on difference sets of relatively dense A \subseteq {1, …, n} How could you potentially have $|A-A|=o(n)$ if nothing prevents $A$ from being the whole set $[1,n]$, or a positive density subset thereof? |
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Jan 30 |
comment |
Constructing expanders in Z/pZ To my understanding, applied to the Problem 7.9 mentioned in my comment above, this explains why $\lambda=O(1)$ does not work - but does not solve the problem in its full generality. Is this correct? |
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Jan 29 |
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Constructing expanders in Z/pZ Not an answer, but certainly related is Problem 7.9 from math.haifa.ac.il/~seva/Papers/montpr.dvi . |
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Jan 14 |
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Simultaneous diophantine approximation Nice proof - much simpler than anything I've seen before. As a point of perfectionism: you may wish to remove extra "such that" and restate the sentence starting with "The statement does not change..." (the statement does change, what you really mean is that replacing the $x_i$ with $nx_i-y_i$ with a suitably chosen $n$ and $y_i$, one can assume without loss of generality that $|x_i|<\epsilon$). |
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Jan 5 |
revised |
Covering all, but $k$ points with affine subspaces added 11 characters in body |
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Jan 5 |
comment |
Covering all, but $k$ points with affine subspaces @domotorp: I know that paper of Alon and Furedi, but this is what I call "easy to see"! Another (an maybe, yet easier) way to get the conclusion is to observe that the complement of a union of $d$ hyperplanes is an intersection of $d$ hyperplanes, hence is given by a system of $d$ linear equations. And, I do not claim that I know a simple proof for $k=1$ and $d$ arbitrary. |
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Jan 5 |
asked | Covering all, but $k$ points with affine subspaces |
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Dec 26 |
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Bipartiteness criterion I had some theoretical application in mind, so I do not care about complexity. Thanks anyway! |
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Dec 24 |
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Lower bound for exponential sums. As far as references are concerned, you can check "On the Littlewood problem modulo a prime" by Green and Konyagin, or the joint papers of Konyagin and myself "Character sums in complex half-planes" and "On the distribution of exponential sums". |
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Dec 24 |
accepted | Lower bound for exponential sums. |
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Dec 24 |
revised |
Lower bound for exponential sums. Typo fixed |
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Dec 24 |
answered | Lower bound for exponential sums. |
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Dec 23 |
comment |
Bipartiteness criterion Thanks - good to know, but not exactly what I am looking for. The definition is that the vertices can be partitioned into two subsets so that no edge is monochromatic, and I need a criterion for this in the spirit of the familiar no-odd-cycles condition. |
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Dec 23 |
asked | Bipartiteness criterion |
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Dec 3 |
revised |
A delicate elementary inequality added 2 characters in body |
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Dec 3 |
awarded | ● Nice Question |
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Dec 3 |
answered | A delicate elementary inequality |
