Open AccessInequalities for permanents and permanental minors of row substochastic matrices
Author(s) -
Zhi Chen,
Jiawei Li,
Lizhen Yang,
Zelin Zhu,
Lei Cao
Publication year - 2019
Publication title -
the electronic journal of linear algebra
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.447
H-Index - 31
eISSN - 1537-9582
pISSN - 1081-3810
DOI - 10.13001/ela.2019.5143
Subject(s) - mathematics , conjecture , convexity , combinatorics , identity matrix , interval (graph theory) , matrix (chemical analysis) , identity (music) , square matrix , inequality , column (typography) , symmetric matrix , eigenvalues and eigenvectors , mathematical analysis , geometry , physics , materials science , quantum mechanics , connection (principal bundle) , acoustics , financial economics , economics , composite material
In this paper, some inequalities for permanents and permanental minors of row substochastic matrices are proved. The convexity of the permanent function on the interval between the identity matrix and an arbitrary row substochastic matrix is also proved. In addition, a conjecture about the permanent and permanental minors of square row substochastic matrices with fixed row and column sums is formulated.