Results 31 to 40 of about 1,277,681 (312)
Polynomial reconstruction of the matching polynomial
Electronic Journal of Graph Theory and Applications, 2015 The matching polynomial of a graph is the generating function of the numbers of its matchings with respect to their cardinality. A graph polynomial is polynomial reconstructible, if its value for a graph can be determined from its values for the vertex-deleted subgraphs of the same graph.
Yongtang Shi, Xueliang Li, Martin Trinks
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A Penrose polynomial for embedded graphs [PDF]
, 2011 We extend the Penrose polynomial, originally defined only for plane graphs, to graphs embedded in arbitrary surfaces. Considering this Penrose polynomial of embedded graphs leads to new identities and relations for the Penrose polynomial which can not be
Aigner +22 more
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Practical polynomial factoring in polynomial time [PDF]
Proceedings of the 36th international symposium on Symbolic and algebraic computation, 2011 State of the art factoring in Q[x] is dominated in theory by a combinatorial reconstruction problem while, excluding some rare polynomials, performance tends to be dominated by Hensel lifting. We present an algorithm which gives a practical improvement (less Hensel lifting) for these more common polynomials.
Hart, William +2 more
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The image of polynomials in one variable on 2×2 upper triangular matrix algebras
AIMS Mathematics, 2022 In the present paper, we give a description of the image of polynomials in one variable on 2×2 upper triangular matrix algebras over an algebraically closed field.
Lan Lu +3 more
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Polynomial selections and separation by polynomials [PDF]
Studia Mathematica, 1996 Necessary and sufficient conditions under which two real functions defined on the real interval can be separated by a polynomial are given. An immediate consequence of the main result is the existence of the polynomial separation of convex functions of higher order. Another application is some Hyers-Ulam-stability-type result.
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SMIRNOV’S INEQUALITY FOR POLYNOMIALS HAVING ZEROS OUTSIDE THE UNIT DISC
Проблемы анализа, 2021 In 1887, the famous chemist D. I. Mendeleev posed the following problem: to estimate |𝑓 ′(𝑥)| for a real polynomial 𝑓 (𝑥), satisfying the condition |𝑓 (𝑥)| ≤ 𝑀 on [𝑎, 𝑏]. This question arose when Mendeleev was studying aqueous solutions.
E. G. Kompaneet, V. V. Starkov
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Polynomial approximation, local polynomial convexity, and degenerate CR singularities [PDF]
, 2006 We begin with the following question: given a closed disc $\bar{D}$ in the complex plane and a complex-valued function F in $C(\bar{D})$, is the uniform algebra on $\bar{D}$ generated by z and F equal to $C(\bar{D})$ ?
Bharali +13 more
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Polynomial Cunningham Chains [PDF]
, 2011 Let $\epsilon\in \{-1,1\}$. A sequence of prime numbers $p_1, p_2, p_3, ...$, such that $p_i=2p_{i-1}+\epsilon$ for all $i$, is called a {\it Cunningham chain} of the first or second kind, depending on whether $\epsilon =1$ or -1 respectively.
Jones, Lenny
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Tutte Polynomials and Link Polynomials [PDF]
Proceedings of the American Mathematical Society, 1988 We show how the Tutte polynomial of a plane graph can be evaluated as the "homfly" polynomial of an associated oriented link. Then we discuss some consequences for the partition function of the Potts model, the Four Color Problem and the time complexity of the computation of the homfly polynomial.
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Generalizations of Chebyshev polynomials and polynomial mappings [PDF]
Transactions of the American Mathematical Society, 2007 In this paper we show how polynomial mappings of degree K \mathfrak {K} from a union of disjoint intervals onto [ − 1 , 1 ] [-1,1] generate a countable number of special cases of generalizations of Chebyshev polynomials.
Yang Chen +3 more
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