Publications of Paul Erdos

Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No: 277.15011
Autor: Erdös, Paul; Minc, Henryk
Title: Diagonals of nonnegative matrices. (In English)
Source: Linear multilinear Algebra 1, 89-95 (1973).
Review: Let (a₁, ... ,a_n), (r₁, ... ,r_n) and (c₁, ... ,c_n) be real n-tuples, n \geq 3, satisfying

sum ⁿ_{i = 1}r_i = sum ⁿ_{i = 1}c_i and 0 \leq a_i \leq max (r_i,c_i), i = 1, ... ,n.

It is shown that a necessary and sufficient condition for the existence of a nonnegative matrix with main diagonal (a₁, ... ,a_n), with row sums r₁, ... ,r_n and column sums c₁, ... ,c_n, is that

sum ⁿ_{i = 1}(r_i-a_i) \geq max_t (r_t+c_t-2a_t).

Equality can hold if and only if all the off-diagonal positive entries of the matrix are restricted to the kth row and the kth column, for some k, 1 \leq k \leq n.
Classif.: * 15A48 Positive matrices and their generalizations
15A45 Miscellaneous inequalities involving matrices
05B20 (0,1)-matrices (combinatorics)

Books Problems Set Theory Combinatorics Extremal Probl/Ramsey Th.

Graph Theory Add.Number Theory Mult.Number Theory Analysis Geometry

Probabability Personalia About Paul Erdös Publication Year Home Page

Books	Problems	Set Theory	Combinatorics	Extremal Probl/Ramsey Th.
Graph Theory	Add.Number Theory	Mult.Number Theory	Analysis	Geometry
Probabability	Personalia	About Paul Erdös	Publication Year	Home Page