A high-tech proof of the Mills-Robbins-Rumsey determinant formula
type: Item
instance of: scholarly article
title: A high-tech proof of the Mills-Robbins-Rumsey determinant formula
zbMATH Open document ID: 0851.05005
author: Herbert S. Wilf
author: Marko Petkovšek
published in: The Electronic Journal of Combinatorics
publication date: 1996-07-21T00:00:00Z
full work available at URL: R19
review text: The formula in question states that \[ \text{det}\Biggl(\Biggl({i+ j+ \mu\atop 2i- j}\Biggr)^{n- 1}_{i, j= 0}\Biggr)= 2^{- n} \prod^{n- 1}_{k= 0} \Delta_{2k}(2\mu), \] where \(\mu\) is an indeterminate, \(\Delta_0(\mu)= 2\) and for \(j= 1,2,\dots\), \[ \Delta_{2j}(\mu)= {(\mu+ 2j+ 2)_j({1\over 2} \mu+ 2j+ {3\over 2})_{j- 1}\over (j)_j ({1\over 2} \mu+ j+ {3\over 2})_{j- 1}}, \] with \((x)_j= x(x+ 1)\cdots (x+ j- 1)\) being the usual rising factorial. We give here a short computer-assisted proof. This proof is conceptually very simple. The intrinsic depth of the problem is reflected only in the very large polynomial that is contained in the proof certificate.
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 15A15
zbMATH DE Number: 907658
zbMATH Keywords: Mills-Robbins-Rumsey determinant formula
zbMATH Keywords: proof certificate
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 907658