# Seva

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## Registered User

 Name Seva Member for 2 years Seen 3 hours ago Website Location Israel Age 50
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 1d awarded ● Nice Question May17 comment Fano plane drawings: embedding PG(2,2) into the real planeHm-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. May16 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. May15 comment Fano plane drawings: embedding PG(2,2) into the real planeSeems it does - very nice! May14 asked Fano plane drawings: embedding PG(2,2) into the real plane May10 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. Apr19 accepted Additive Combinatorics - reference request Apr19 comment Additive Combinatorics - reference requestNot that I could recall it, at least... Apr19 answered Additive Combinatorics - reference request Apr15 accepted Perimeter/Neighborhood of a graph on grid Apr14 revised Perimeter/Neighborhood of a graph on gridTags edited Apr14 answered Perimeter/Neighborhood of a graph on grid Mar26 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 $g^{\pm1}z$)? Mar25 revised More expanders?added 32 characters in body; deleted 3 characters in body Mar25 comment More expanders?The argument for the second graph is really nice, thanks! Mar22 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? Mar22 comment 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? :-) ) Mar22 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. Mar22 asked More expanders? Mar20 awarded ● Notable Question Mar17 comment An expander (?) graphSorry for being unable to accept both answers... Thanks, anyway! Mar16 asked An expander (?) graph Mar6 answered Formal writing: numbers under 10 Feb18 comment nonnegative Fourier TransformWhat do you call "the other inequality" and where your question originates from? Feb11 comment A sum involving mod(n) arithmeticThe sum of WHAT, and what exactly is your question? Feb11 comment Minimum number of solutions in a system of equalities and non-equalitiesHow about fixing the typo(s) and motivating your question to convince the community that this is not a homework problem? Feb10 comment 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. Feb7 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? Jan30 comment Constructing expanders in Z/pZTo 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? Jan29 comment Constructing expanders in Z/pZNot an answer, but certainly related is Problem 7.9 from math.haifa.ac.il/~seva/Papers/montpr.dvi . Jan14 comment Simultaneous diophantine approximationNice 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 $|x_i|<\epsilon$). Jan5 revised Covering all, but $k$ points with affine subspacesadded 11 characters in body Jan5 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. Jan5 asked Covering all, but $k$ points with affine subspaces Dec26 comment Bipartiteness criterionI had some theoretical application in mind, so I do not care about complexity. Thanks anyway! Dec24 comment 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". Dec24 accepted Lower bound for exponential sums. Dec24 revised Lower bound for exponential sums.Typo fixed Dec24 answered Lower bound for exponential sums. Dec23 comment Bipartiteness criterionThanks - 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. Dec23 asked Bipartiteness criterion Dec3 revised A delicate elementary inequalityadded 2 characters in body Dec3 awarded ● Nice Question Dec3 answered A delicate elementary inequality