scholarly journals Can Sylvester's determinantal identity, equivalently Muir's law of extensible minors be generalized?

2015 ◽  
Vol 482 ◽  
pp. 70-83 ◽  
Author(s):  
André Pierro de Camargo ◽  
Felipe da Silva Alves
Keyword(s):  
Determinantal Identity

scholarly journals Arithmetic–Geometric Mean determinantal identity

2011 ◽  
Vol 435 (11) ◽  
pp. 2936-2941
Author(s):  
M. Bayat ◽  
H. Teimoori
Keyword(s):  
Geometric Mean ◽  
Determinantal Identity

scholarly journals A Determinant of the Chudnovskys Generalizing the Elliptic Frobenius-Stickelberger-Cauchy Determinantal Identity

10.37236/1544 ◽  
2000 ◽  
Vol 7 (1) ◽  
Author(s):  
Tewodros Amdeberhan
Keyword(s):  
Elliptic Functions ◽  
Analytic Proof ◽  
Determinantal Identity

D.V. Chudnovsky and G.V. Chudnovsky [CH] introduced a generalization of the Frobenius-Stickelberger determinantal identity involving elliptic functions that generalize the Cauchy determinant. The purpose of this note is to provide a simple essentially non-analytic proof of this evaluation. This method of proof is inspired by D. Zeilberger's creative application in [Z1].

Walk Generating Functions, Christoffel-Darboux Identities and the Adjacency Matrix of a Graph

1992 ◽  
Vol 1 (1) ◽  
pp. 13-25 ◽  
Author(s):  
C. D. Godsil
Keyword(s):  
Orthogonal Polynomials ◽  
Characteristic Polynomial ◽  
Generating Functions ◽  
Adjacency Matrix ◽  
Characteristic Polynomials ◽  
Combinatorial Interpretation ◽  
Determinantal Identity

In this work we show that that many of the basic results concerning the theory of the characteristic polynomial of a graph can be derived as easy consequences of a determinantal identity due to Jacobi. As well as improving known results, we are also able to derive a number of new ones. A combinatorial interpretation of the Christoffel-Darboux identity from the theory of orthogonal polynomials is also presented. Finally, we extend some work of Tutte on the reconstructibility of graphs with irreducible characteristic polynomials.

scholarly journals Viewing Determinants as Nonintersecting Lattice Paths yields Classical Determinantal Identities Bijectively

10.37236/2530 ◽  
2012 ◽  
Vol 19 (3) ◽  
Author(s):  
Markus Fulmek
Keyword(s):  
Generating Functions ◽  
Point Of View ◽  
Lattice Paths ◽  
Binet Formula ◽  
Plücker Relations ◽  
Nonintersecting Lattice Paths ◽  
Determinantal Identities ◽  
Determinantal Identity

In this paper, we show how general determinants may be viewed as generating functions of nonintersecting lattice paths, using the Lindström-Gessel-Viennot-method and the Jacobi Trudi identity together with elementary observations.After some preparations, this point of view provides "graphical proofs'' for classical determinantal identities like the Cauchy-Binet formula, Dodgson's condensation formula, the Plücker relations, Laplace's expansion and Turnbull's identity. Also, a determinantal identity generalizing Dodgson's condensation formula is presented, which might be new.

scholarly journals q-Stirling Identities Revisited

10.37236/6829 ◽  
2018 ◽  
Vol 25 (1) ◽  
Author(s):  
Yue Cai ◽  
Richard Ehrenborg ◽  
Margaret Readdy
Keyword(s):  
Symmetric Function ◽  
Theoretic Proof ◽  
Two Parameter ◽  
Determinantal Identity

We give combinatorial proofs of q-Stirling identities using restricted growth words.  This includes a poset theoretic proof of Carlitz's identity, a new proof of the q-Frobenius identity of Garsia and Remmel and of Ehrenborg's Hankel q-Stirling determinantal identity.  We also develop a two parameter generalization to unify identities of Mercier and include a symmetric function version.

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