scholarly journals Random integral matrices and the Cohen-Lenstra heuristics

2019 ◽  
Vol 141 (2) ◽  
pp. 383-398 ◽  
Author(s):  
Melanie Matchett Wood
Keyword(s):  
Integral Matrices ◽  
Random Integral

scholarly journals Fermat's type equations in the set of 2×2 integral matrices

1998 ◽  
Vol 22 (3) ◽  
pp. 637-643
Author(s):  
Zhenfu Cao ◽  
Aleksander Grytczuk
Keyword(s):  
Integral Matrices

scholarly journals A note on integral matrices associated to finite fields

1988 ◽  
Vol 114 (2) ◽  
pp. 477-478
Author(s):  
Jacob Nemchenok
Keyword(s):  
Finite Fields ◽  
Integral Matrices

scholarly journals Additivity obstructions for integral matrices and pyramids

2008 ◽  
Vol 406 (1-2) ◽  
pp. 136-145 ◽  
Author(s):  
Miguel Santoyo ◽  
Ernesto Vallejo
Keyword(s):  
Integral Matrices

scholarly journals Non-negative integral matrices with given spectral radius and controlled dimension

2021 ◽  
pp. 1-24
Author(s):  
MEHDI YAZDI
Keyword(s):  
Spectral Radius ◽  
Positive Real Number ◽  
Algebraic Integer ◽  
Log P ◽  
Irreducible Matrix ◽  
Positive Real ◽  
Shift Of Finite Type ◽  
Primitive Matrix ◽  
Integral Matrices ◽  
Perron Number

Abstract A celebrated theorem of Douglas Lind states that a positive real number is equal to the spectral radius of some integral primitive matrix, if and only if, it is a Perron algebraic integer. Given a Perron number p, we prove that there is an integral irreducible matrix with spectral radius p, and with dimension bounded above in terms of the algebraic degree, the ratio of the first two largest Galois conjugates, and arithmetic information about the ring of integers of its number field. This arithmetic information can be taken to be either the discriminant or the minimal Hermite-like thickness. Equivalently, given a Perron number p, there is an irreducible shift of finite type with entropy $\log (p)$ defined as an edge shift on a graph whose number of vertices is bounded above in terms of the aforementioned data.

scholarly journals Constructing integral matrices with given line sums

2009 ◽  
Vol 431 (9) ◽  
pp. 1553-1563 ◽  
Author(s):  
J.A. Dias da Silva ◽  
Amélia Fonseca
Keyword(s):  
Integral Matrices

FORMULAS FOR THE CASSON INVARIANT OF CERTAIN INTEGRAL HOMOLOGY 3-SPHERES

2009 ◽  
Vol 18 (11) ◽  
pp. 1551-1576 ◽  
Author(s):  
SANG YOUL LEE ◽  
MYOUNGSOO SEO
Keyword(s):  
Explicit Formula ◽  
Dehn Surgery ◽  
Integral Homology ◽  
Integral Matrices ◽  
Knots And Links ◽  
Special Classes

In this paper, we introduce a representation of knots and links in S3 by integral matrices and then give an explicit formula for the Casson invariant for integral homology 3-spheres obtained from S3 by Dehn surgery along the knots and links represented by the integral matrices in which either all entries are even or the entries of each row are the same odd number. As applications, we study the preimage of the Casson invariant for a given integer and also give formulas for the Casson invariants of some special classes of integral homology 3-spheres.

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