Results 41 to 50 of about 4,716 (302)
Some fundamental Fibonacci number congruences [PDF]
Notes on Number Theory and Discrete MathematicsThis paper investigates a number of congruence properties related to the coefficients of a generalized Fibonacci polynomial. This polynomial was defined to produce properties comparable with those of the standard polynomials of some special functions ...
Anthony G. Shannon +3 more
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Mathematics, 2020 An arbitrary univariate polynomial of nth degree has n sequences. The sequences are systematized into classes. All the values of the first class sequence are obtained by Newton’s polynomial of nth degree. Furthermore, the values of all sequences for each
Ilija Tanackov +2 more
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Generalized monotone triangles [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 In a recent work, the combinatorial interpretation of the polynomial $\alpha (n; k_1,k_2,\ldots,k_n)$ counting the number of Monotone Triangles with bottom row $k_1 < k_2 < ⋯< k_n$ was extended to weakly decreasing sequences $k_1 ≥k_2 ≥⋯≥k_n$.
Lukas Riegler
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On derandomizing tests for certain polynomial identities [PDF]
, 2003 We extract a paradigm for derandomizing tests for polynomial identities from the recent AKS primality testing algorithm.
Agrawal, Manindra
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Polynomial identities for partitions
European Journal of Combinatorics, 1992 Set \(P_ 1(q)=1-q\) and \(P_ k(q)=\sum_{d\mid k}\mu(k/d)\) for \(k>1\). For every integer \(m>1\) define \[ P^ +_{k,m}(q)=P_ k(q)(P_ k(q)+k)(P_ k(q)+2k)\cdots(P_ k(q)+(m-1)k), \] \[ P^ -_{k,m}(q)=P_ k(q)(P_ k(q)-k)(P_ k(q)-2k)\cdots(P_ k(q)-(m-1)k); \] and set \(P^ +_{k,0}(q)=P^ -_{k,0}(q)=1\).
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Generalized Pseudospectral Method and Zeros of Orthogonal Polynomials
Advances in Mathematical Physics, 2018 Via a generalization of the pseudospectral method for numerical solution of differential equations, a family of nonlinear algebraic identities satisfied by the zeros of a wide class of orthogonal polynomials is derived.
Oksana Bihun, Clark Mourning
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MacWilliams Identities and Matroid Polynomials [PDF]
The Electronic Journal of Combinatorics, 2002 We present generalisations of several MacWilliams type identities, including those by Kløve and Shiromoto, and of the theorems of Greene and Barg that describe how the Tutte polynomial of the vector matroid of a linear code determines the $r$th support weight enumerators of the code.
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Polynomial identities in nil-algebras [PDF]
Transactions of the American Mathematical Society, 2009 A polynomial identity is called `Specht' if every system containing this identity has a finite basis. By a theorem of Kemer, over a field of characteristic 0, every system of polynomial identities of associative algebras is finitely based. Recently, Belov, Grishin and Shchigolev proved that over a field of prime characteristic \(p>0\) there are non ...
Aladova, Elena V. +1 more
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New fractional approaches for n-polynomial P-convexity with applications in special function theory
Advances in Difference Equations, 2020 Inequality theory provides a significant mechanism for managing symmetrical aspects in real-life circumstances. The renowned distinguishing feature of integral inequalities and fractional calculus has a solid possibility to regulate continuous issues ...
Shu-Bo Chen +4 more
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A glimpse into the Asymptotics of polynomial identities
, 2017 This a survey paper on the most significant results in the combinatorial theory of polynomial identities.
Janssens, Geoffrey
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