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A Combinatorial Identity and the World Series
SIAM Review, 1993In this note the author gives a simple probabilistic proof of a combinatorial identity by calculating the winning probability in the World Series. The winning probabilities and the expected length of the championship series are given by the applications of the identity and its generalization.
Tamás Lengyel
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A new approach for proving or generating combinatorial identities
International Journal of Mathematical Education in Science and Technology, 2010 A new method for proving, in an immediate way, many combinatorial identities is presented. The method is based on a simple recursive combinatorial formula involving n+1 arbitrary real parameters.
Luis González
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A Family of Combinatorial Identities
Canadian Mathematical Bulletin, 1972In a recent paper, Murray Eden [5] generalized the simple identity for the Eulerian product,1.1and obtained the following infinite family of identities:For A= 1,2, 3,…, let1.2where we assume throughout that |x| < 1, empty products equal unity and empty sums equal zero; then1.3As Eden noted, Fh(b;x) is the generating function of ph(m, n) which ...
Andrews, G. E. +2 more
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COMBINATORIAL IDENTITIES AND HYPERGEOMETRIC FUNCTIONS
Rocky Mountain Journal of Mathematics, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Alzer, Horst, Richards, Kendall C.
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On two combinatorial identities
Journal of Computational Methods in Sciences and Engineering, 2017Two combinatorial identities are proved. The first one allows easy to establish connections between Bernoulli and Stirling numbers and values of zeta function of integer arguments and to find numerous identities, including the new ones, for these quantities.
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Publicationes Mathematicae Debrecen, 2022
The author proves that the only solution of the difference equation \[ \Phi (2(v+1))+\sum^{v}_{k=1}\binom{2v}{2k-1} \Phi (2k) \Phi (2(v-k+1))=0 \] subject to the initial condition \(\Phi (2)=1/4\) is \(\Phi (2k)=((2^{2k}-1)/2k) B_{2k}\) where the \(B_{2k}\) are the even-indexed Bernoulli numbers. Using this result, he then proves that (1/k)\(| B_{2k}|^{
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The author proves that the only solution of the difference equation \[ \Phi (2(v+1))+\sum^{v}_{k=1}\binom{2v}{2k-1} \Phi (2k) \Phi (2(v-k+1))=0 \] subject to the initial condition \(\Phi (2)=1/4\) is \(\Phi (2k)=((2^{2k}-1)/2k) B_{2k}\) where the \(B_{2k}\) are the even-indexed Bernoulli numbers. Using this result, he then proves that (1/k)\(| B_{2k}|^{
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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, 2012zbMATH 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, 2005zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Egorychev, Georgy P. +1 more
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