Bounds on the Number of Real Solutions to Polynomial Equations
نویسندگان
چکیده
منابع مشابه
Bounds on the number of real solutions to polynomial equations
We use Gale duality for polynomial complete intersections and adapt the proof of the fewnomial bound for positive solutions to obtain the bound e + 3 4 2( k 2)nk for the number of non-zero real solutions to a system of n polynomials in n variables having n+k+1 monomials whose exponent vectors generate a subgroup of Z of odd index. This bound exceeds the bound for positive solutions only by the ...
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15 صفحه اولLower Bounds for Real Solutions to Sparse Polynomial Systems
We show how to construct sparse polynomial systems that have non-trivial lower bounds on their numbers of real solutions. These are unmixed systems associated to certain polytopes. For the order polytope of a poset P this lower bound is the sign-imbalance of P and it holds if all maximal chains of P have length of the same parity. This theory also gives lower bounds in the real Schubert calculu...
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NOTE: Unfortunately, most of the results mentioned here were already known under the name of ”d-separated interval piercing”. The result that Td(m) exists was first proved by Gyárfás and Lehel in 1970, see [5]. Later, the result was strengthened by Károlyi and Tardos [9] to match our result. Moreover, their proof (in a different notation, of course) uses ideas very similar to ours and leads to ...
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ardy and Littlewood conjectured that every large integer $n$ that is not a square is the sum of a prime and a square. They believed that the number $mathcal{R}(n)$ of such representations for $n = p+m^2$ is asymptotically given by begin{equation*} mathcal{R}(n) sim frac{sqrt{n}}{log n}prod_{p=3}^{infty}left(1-frac{1}{p-1}left(frac{n}{p}right)right), end{equation*} where $p$ is a prime, $m$ is a...
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ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2010
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rnm114