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Mills-Robbins-Rumsey Determinant Formula

det(i+j+mu; 2i-j)_(i,j=0)^(n-1)=2^(-n)product_(k=0)^(n-1)Delta_(2k)(2mu),

where mu is an indeterminate, Delta_0(mu)=2,

Delta_(2j)(mu)=((mu+2j+2)_j(1/2mu_2j+3/2)_(j-1))/((j)_j(1/2mu+j+3/2)_(j-1)),

for j=1, 2, ..., and (x)_j=x(x+1)...(x+j-1) is the rising factorial (Mills et al. 1987, Andrews and Burge 1993).

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References

Andrews, G. E. and Burge, W. H. "Determinant Identities." Pacific J. Math. 158, 1-14, 1993.Mills, W. H.; Robbins, D. P.; and Rumsey, H. Jr. "Enumeration of a Symmetry Class of Plane Partitions." Discrete Math. 67, 43-55, 1987.Petkovšek, M. and Wilf, H. S. "A High-Tech Proof of the Mills-Robbins-Runsey Determinant Formula." Electronic J. Combinatorics 3, No. 2, R19, 1-3, 1996. http://www.combinatorics.org/Volume_3/Abstracts/v3i2r19.html.

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Mills-Robbins-Rumsey Determinant Formula

Cite this as:

Weisstein, Eric W. "Mills-Robbins-Rumsey Determinant Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Mills-Robbins-RumseyDeterminantFormula.html

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