scholarly journals Sign patterns of rational matrices with large rank

2014 ◽  
Vol 42 ◽  
pp. 107-111 ◽  
Author(s):  
Yaroslav Shitov
Keyword(s):  
Large Rank ◽  
Sign Patterns

scholarly journals Sign patterns of rational matrices with large rank II

2022 ◽  
pp. 63-64
Author(s):  
Yaroslav Shitov
Keyword(s):  
General Result ◽  
Recent Literature ◽  
Sign Pattern ◽  
Large Rank ◽  
Sign Patterns

It is known that, for any real m-by-n matrix A of rank n-2, there is a rational m-by-n matrix which has rank n-2 and sign pattern equal to that of  A. We prove a more general result conjectured in the recent literature.  

scholarly journals A diameter bound for finite simple groups of large rank

2017 ◽  
Vol 95 (2) ◽  
pp. 455-474 ◽  
Author(s):  
Arindam Biswas ◽  
Yilong Yang
Keyword(s):  
Simple Groups ◽  
Finite Simple Groups ◽  
Large Rank

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 $1$ .

scholarly journals Elliptic Curves with Large Rank over Function Fields

2002 ◽  
Vol 155 (1) ◽  
pp. 295 ◽  
Author(s):  
Douglas Ulmer
Keyword(s):  
Elliptic Curves ◽  
Function Fields ◽  
Large Rank

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 Small Degree Representations of Finite Chevalley Groups in Defining Characteristic

2001 ◽  
Vol 4 ◽  
pp. 135-169 ◽  
Author(s):  
Frank Lübeck
Keyword(s):  
Algebraic Groups ◽  
Small Degree ◽  
Irreducible Representations ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Linear Algebraic Groups ◽  
Large Rank ◽  
Projective Representations ◽  
Computer Calculations ◽  
Simply Connected

AbstractThe author has determined, for all simple simply connected reductive linear algebraic groups defined over a finite field, all the irreducible representations in their defining characteristic of degree below some bound. These also give the small degree projective representations in defining characteristic for the corresponding finite simple groups. For large rank l, this bound is proportional to l3, and for rank less than or equal to 11 much higher. The small rank cases are based on extensive computer calculations.

RANDOM (r, s)-GENERATION OF FINITE CLASSICAL GROUPS

2002 ◽  
Vol 34 (2) ◽  
pp. 185-188 ◽  
Author(s):  
MARTIN W. LIEBECK ◽  
ANER SHALEV
Keyword(s):  
Classical Groups ◽  
Large Rank ◽  
Finite Classical Groups

A proof is given that for primes r, s, not both 2, and for finite simple classical groups G of sufficiently large rank, the probability that two randomly chosen elements in G of orders r and s generate G tends to 1 as |G| → ∞.

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