scholarly journals Counterexamples on spectra of sign patterns

2018 ◽  
Vol 146 (9) ◽  
pp. 3709-3713
Author(s):  
Yaroslav Shitov
Keyword(s):  
Sign Patterns

scholarly journals Sarnak’s conjecture for sequences of almost quadratic word growth

2020 ◽  
pp. 1-56
Author(s):  
REDMOND MCNAMARA
Keyword(s):  
Box Dimension ◽  
Multiplicative Functions ◽  
Logarithmic Density ◽  
Liouville Function ◽  
Sign Patterns

Abstract We prove the logarithmic Sarnak conjecture for sequences of subquadratic word growth. In particular, we show that the Liouville function has at least quadratically many sign patterns. We deduce the main theorem from a variant which bounds the correlations between multiplicative functions and sequences with subquadratically many words which occur with positive logarithmic density. This allows us to actually prove that our multiplicative functions do not locally correlate with sequences of subquadratic word growth. We also prove a conditional result which shows that if the ( $\kappa -1$ )-Fourier uniformity conjecture holds then the Liouville function does not correlate with sequences with $O(n^{t-\varepsilon })$ many words of length n where $t = \kappa (\kappa +1)/2$ . We prove a variant of the $1$ -Fourier uniformity conjecture where the frequencies are restricted to any set of box dimension less than $1$ .

Stability of sign patterns from a system of second order ODEs

2021 ◽  
Author(s):  
Adam H. Berliner ◽  
Minerva Catral ◽  
D.D. Olesky ◽  
P. van den Driessche
Keyword(s):  
Second Order ◽  
Sign Patterns

Bounds on the local bases of primitive nonpowerful nearly reducible sign patterns

2009 ◽  
Vol 57 (2) ◽  
pp. 205-215 ◽  
Author(s):  
Yubin Gao ◽  
Yanling Shao ◽  
Jian Shen
Keyword(s):  
Sign Patterns

scholarly journals On realizability of sign patterns by real polynomials

2018 ◽  
Vol 68 (3) ◽  
pp. 853-874 ◽  
Author(s):  
Vladimir Kostov
Keyword(s):  
Real Polynomials ◽  
Sign Patterns

scholarly journals Sign patterns that require or allow power-positivity

2009 ◽  
Vol 19 ◽  
Author(s):  
Minerva Catral ◽  
Leslie Hogben ◽  
Dale Olesky ◽  
Pauline Van den Driessche
Keyword(s):  
Sign Patterns

scholarly journals Sign patterns that require eventual exponential nonnegativity

2015 ◽  
Vol 30 ◽  
Author(s):  
Craig Erickson
Keyword(s):  
Sign Pattern ◽  
Sign Patterns ◽  
Necessary And Sufficient

Sign patterns that require exponential nonnegativity are characterized. A set of conditions necessary for a sign pattern to require eventual exponential nonnegativity are established. It is shown that these conditions are also sufficient for an upper triangular sign pattern to require eventual exponential nonnegativity and it is conjectured that these conditions are both necessary and sufficient for any sign pattern to require eventual exponential nonnegativity. It is also shown that the maximum number of negative entries in a sign pattern that requires eventual exponential nonnegativity is (n−1)(n−2)/2 + 2

scholarly journals The potentially stable tree sign patterns for dimensions less than five

1989 ◽  
Vol 126 ◽  
pp. 1-13 ◽  
Author(s):  
Charles R. Johnson ◽  
Tracy A. Summers
Keyword(s):  
Sign Patterns ◽  
Stable Tree

The sepr-sets of sign patterns

2019 ◽  
Vol 68 (10) ◽  
pp. 2044-2068
Author(s):  
Leslie Hogben ◽  
Jephian C.-H. Lin ◽  
D.D. Olesky ◽  
P. van den Driessche
Keyword(s):  
Sign Patterns
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