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Vertex Algebras and Combinatorial Identities [PDF]

Acta Applicandae Mathematica, 2002
In 1980's J. Lepowsky and R. Wilson gave a Lie-theoretic interpretation of Rogers-Ramanujan identities in terms of level 3 representations of affine Lie algebra sl(2, C)~. When applied to other representations and affine Lie algebras, Lepowsky-Wilson's approach yielded series of other combinatorial identities of Rogers-Ramanujan type. At about the same
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Some Combinatorial and Analytical Identities

Annals of Combinatorics, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ismail, Mourad E.H., Stanton, Dennis
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The Combinatorial Identity on the Jacobian Conjecture

Acta Applicandae Mathematicae, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Egorychev, Georgy P., Stepanenko, Vitaly A.   +1 more
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Three Identities in Combinatory Analysis

Journal of the London Mathematical Society, 1943
Es sei \[ x_n = 1 - x^n, \quad \bar x_n = 1 + x^n, \quad x_n!= \prod_{i=1}^n x_i, \quad \bar x_n! = \prod_{i=1}^n \bar x_i, \] \[ x_n^2 = x_{2n}, \quad x_n^2! = x_2x_4\ldots x_{2n}, \quad x! = x_\infty !,\quad \bar x! = \bar x_\infty!, \quad x^2! = x_\infty^2!, \] dann beweist der Verf.
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Zeon Algebra and Combinatorial Identities

SIAM Review, 2014
We show that the ordinary derivative of a real analytic function of one variable can be realized as a Grassmann--Berezin-type integration over the Zeon algebra, the Z-integral. As a by-product of this representation, we give new proofs of the Faa di Bruno formula and Spivey's identity [M. Z. Spivey, J.
Antônio Francisco Neto, Petrus H. R. dos Anjos   +1 more
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Identities for Combinatorial Extremal Theory

Bulletin of the London Mathematical Society, 1997
This paper proves new Ahlswede-Zhang type identities for finite set systems.
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Divided Differences and Combinatorial Identities

Studies in Applied Mathematics, 1991
We present an algebraic theory of divided differences which includes confluent differences, interpolation formulas, Liebniz's rule, the chain rule, and Lagrange inversion. Our approach uses only basic linear algebra. We also show that the general results about divided differences yield interesting combinatorial identities when we consider some suitable
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Some Combinatorial Identities of Bernstein

SIAM Journal on Mathematical Analysis, 1978
For g a rational integer such that $\Delta = 4g^3 + 27$ is square-free, let w denote the real root of $u^3 + gu - 1 = 0$ and put $w^n = r_n + s_n w + t_n w^2 $, $w^{ - n} = x_n + y_n w + z_n w^2 $, $n \geqq 0$. Making use of the theory of units in an algebraic number field, Bernstein obtained quadratic relations involving the $r_n $ and $x_n $ as well ...
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Inversion Techniques and Combinatorial Identities

1994
The purpose of this article is to emphasize the usefulness of inverse relations in order to derive (possibly) new identities from known ones. This method was made popular by \textit{J. Riordan} [``Combinatorial identities'' (1968; Zbl 0194.005)]. Suppose tht \((M_{nk})_{n,k\geq 0}\) and \((M^{-1}_{nk})_{n,k\geq 0}\) are (infinite-dimensional) lower ...
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Combinatorial Identities

Technometrics, 1969
J. Gani, J. Riordan
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