Applications of stable polynomials to mixed determinants: Johnson's conjectures, unimodality, and symmetrized Fischer products

By Julius Borcea, Petter Brand'en. 2006

93 citations recorded by the source corpus.

For (n x n)-matrices A and B, define eta(A, B) = Sigma(S)det(A[S])det(B[S']), where the summation is over all subsets of {1,..., n}, S' is the complement of S', and A [S] is the principal submatrix ...

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1055172dfc8f4c35bbe5b2e70fae8cdde95c052b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Petter Brand'en
2. Julius Borcea
3. David G. Wagner
4. Robin Pemantle
5. Thomas M. Liggett
6. Daniel A. Spielman
7. Nikhil Srivastava
8. Adam W. Marcus

In Computational Theory and Mathematics

1. Julius Borcea
2. Petter Brand'en
3. David G. Wagner
4. Adam W. Marcus
5. Nikhil Srivastava
6. Daniel A. Spielman
7. Liam Solus
8. Tim Netzer

In Geometry and Topology

1. Petter Brand'en
2. Julius Borcea
3. David G. Wagner
4. Thomas M. Liggett
5. Adam W. Marcus
6. Nikhil Srivastava
7. Daniel A. Spielman

Citations in the corpus

• Multivariate Pólya–Schur classification problems in the Weyl algebra (2006, methodology): “The second author is grateful to The Mittag-Leffler Institute forits hospitality in Spring 2005 when this and related projects [9, 10 , 12, 15] were started.”
• The Lee-Yang and Pólya-Schur programs. I. Linear operators preserving stability (2008, background): “This also illustrates Hinkkanen’s observations about zeros of multivariate polynomials and their “so far unnoticed connections to various other concepts in mathematics” [23], which are further substantiated by recent applications to probability theory, matrix theory and combinatorics [ 6 , 10, 12, 1”