Power series with positive coefficients arising from the characteristic polynomials of positive matrices
Let A be an n × n (entrywise) positive matrix and let f ( t ) = det ( I - t A ) . We prove the surprising result that there always exists a positive integer N such that the formal power series expansion of 1 - f ( t ) 1 / N around t = 0 has positive coefficients.
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| Veröffentlicht in: | Mathematische annalen 2016-02, Vol.364 (1-2), p.687-707 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Let
A
be an
n
×
n
(entrywise) positive matrix and let
f
(
t
)
=
det
(
I
-
t
A
)
. We prove the surprising result that there always exists a positive integer
N
such that the formal power series expansion of
1
-
f
(
t
)
1
/
N
around
t
=
0
has positive coefficients. |
|---|---|
| ISSN: | 0025-5831 1432-1807 |
| DOI: | 10.1007/s00208-015-1233-9 |