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Hall exponents of matrices, tournaments and their line digraphs

2011
*
Czechoslovak Mathematical Journal
*

We now show that the upper

doi:10.1007/s10587-011-0066-2
fatcat:l4ague2v7jfm7n3rpx6fyfnydm
*bound**for*the Hall*exponent*in Theorem 4.6 cannot be improved by much, by obtaining a lower*bound**for*the Hall*exponent**of*the line digraph*of*the special*tournament*T * n . ... In [12] , it is stated that the*primitive**exponent**of*a regular or nearly regular*tournament**of*order n is 3*for*n 7. ... K i e r n a n, Department*of*Mathematics, University*of*Wisconsin, Madison, WI 53706 USA, e-mails: brualdi@ math.wisc.edu, kiernan@math.wisc.edu. ...##
###
Page 596 of Mathematical Reviews Vol. , Issue 93b
[page]

1993
*
Mathematical Reviews
*

In this paper, we first obtain an upper

*bound**for*o,(G) and determine the structure*of*a*2*-connected graph G when o,(G) attains the*bound*. ... Let NE, be the set*of**exponents**of**primitive*, minimally strong digraphs*of*order n. ...##
###
Page 283 of Mathematical Reviews Vol. 41, Issue 2
[page]

1971
*
Mathematical Reviews
*

We say M20 is

*primitive*if M'>0*for*some positive integer ¢, the smallest such ¢ being the*exponent**of*M. § 13. The powers*of**tournament*matrices. ... If T', (n*2*5) is irreducible then 7’, (i.e., M(7’,)) is*primitive*, and d<e<d+3, where d is the diameter*of*7’, and e the*exponent**of*M(T’,).§ § 14. Scheduling a*tournament*. ...##
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Generalized exponents of boolean matrices

2003
*
Linear Algebra and its Applications
*

Graph Theory 14 (1990) 483) introduced the concept

doi:10.1016/s0024-3795(02)00714-0
fatcat:j7fzqzadv5cjhizr4igwrrrcje
*of*generalized*exponent**for**primitive*Boolean matrices. ... In the study*of*generalized*exponents*, we focus on problems*of*the following three types: (1) To determine the maxima (namely, the exact upper*bounds*)*of*all kinds*of*generalized*exponents*; (*2*) To characterize ... Jai-yu Shao*for*valuable suggestions. ...##
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Page 2607 of Mathematical Reviews Vol. , Issue 96e
[page]

1996
*
Mathematical Reviews
*

The

*extremal*exhaustive graphs are determined*for*n > 7.” ... Summary: “Let MD,(n) = {D| D is a*primitive*ministrong di- graph with » vertices, and the shortest cycle length*of*D is s}, and b,(n) = max{y(D)| D € MD,(n)}, where y(D) is the*primitive**exponent**of*D. ...##
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Page 1721 of Mathematical Reviews Vol. , Issue 84e
[page]

1984
*
Mathematical Reviews
*

However, formula (

*2*) in the paper is printed in a misleading way in that the term*2*( p— 1)/d should be an*exponent**of*(1 + x??*). ... 1721 OSC Graph theory vertex set is the collection*of*all faces*of*K, and*for*two the vertices are all the*extreme*rays*of*K. ...##
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Page 5763 of Mathematical Reviews Vol. , Issue 95j
[page]

1995
*
Mathematical Reviews
*

Pullman, A

*bound*on the*exponent**of*a*primitive*matrix using Boolean rank (101-116); Karl Gustafson, Matrix trigonometry (117-140); Douglas Hale and George Lady, Qualitative comparative statics and audits ... Sidorenko], An analytic approach to*extremal*problems*for*graphs and hypergraphs (423-455); W. T. ...##
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MAXIMAL EXPONENTS OF PRIMITIVE GRAPHS WITH MINIMUM DEGREE 3

2011
*
Korean Journal of Mathematics
*

In this paper, we find the maximum

doi:10.11568/kjm.2011.19.4.367
fatcat:ygwa2f45bvbo5cmfxd5f3jem44
*exponent**of**primitive*simple graphs G under the restriction deg(v) ≥ 3*for*all vertex v*of*G. ... Our result is also an answer*of*a Klee and Quaife type problem on*exponent*to find minimum number*of*vertices*of*graphs which have fixed even*exponent*and the degree*of*whose vertices are always at least ... Moreover this upper*bound*is*extremal**for*n ≥ 8, i.e.,*for*each n ≥ 8, there is a*primitive*graph on n vertices with minimum degree 3 and*exponent*the smallest value*of*above inequality. ...##
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Generalized exponents of primitive symmetric digraphs

1997
*
Discrete Applied Mathematics
*

*For*such a digraph there is a minimum integer t, called the

*exponent*

*of*D, such that given any ordered pair

*of*vertices x and y there is a directed walk from x to y

*of*length t. ... In this paper we determine the largest value

*of*these generalized

*exponents*over the set

*of*

*primitive*symmetric digraphs whose shortest odd cycle length is a fixed number r. ... In [l, 3,4] Brualdi and Liu derived upper

*bounds*

*for*the generalized

*exponents*

*of*

*primitive*digraphs and

*for*

*primitive*digraphs

*of*special type (symmetric digraphs,

*tournaments*, and minimally strong digraphs ...

##
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Toward automating EA configuration: the parent selection stage

2007
*
2007 IEEE Congress on Evolutionary Computation
*

One

doi:10.1109/cec.2007.4424455
dblp:conf/cec/SmorodkinaT07
fatcat:zbfm7txexrdhfoxeuvqwqgsuxy
*of*the obstacles to Evolutionary Algorithms (EAs) fulfilling their promise as easy to use general-purpose problem solvers, is the difficulty*of*correctly configuring them*for*specific problems such ... Having a mechanism*for*automatically configuring parameters and operators*of*every stage*of*the evolutionary life-cycle would give EAs a more widely spread popularity in the non-expert community. ...*Primitive*name Description*Tournament*Selection standard deterministic*tournament*selection with*tournament*size*of*5 Roulette Selection standard roulette selection Random Selection a routine that uniform ...##
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Maximal exponents of polyhedral cones (III)

2013
*
Transactions of the American Mathematical Society
*

It is proved that

doi:10.1090/s0002-9947-2013-05879-5
fatcat:frtl2y33avgynfhyh24ozrqhxa
*for*any positive integers m, n, 3 ≤ n ≤ m, the maximum value*of*γ(K), as K runs through all n-dimensional polyhedral cones with m*extreme*rays, equals (n − 1)(m − 1) + 1*2*1 + (−1) (n ...*For*a polyhedral cone K, the maximum value*of*γ(A), taken over all K-*primitive*matrices A, is denoted by γ(K). ... Acknowledgements The first and third authors would like to thank Hans Schneider and Sergeǐ Sergeev*for*drawing their attention to the work*of*Grinberg [11] . ...##
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The scrambling index of primitive digraphs

2010
*
Computers and Mathematics with Applications
*

In this paper, we obtain some new upper

doi:10.1016/j.camwa.2010.05.018
fatcat:kppiho5i7jhxdliqxllruk6ybi
*bounds**for*the scrambling index*of**primitive*digraphs. ... Moreover, the maximum index problem, the*extremal*matrix problem and the index set problem*for*the scrambling index*of*various classes*of**primitive*digraphs (e.g.*primitive*digraphs with d loops, minimally ... Acknowledgements The authors are grateful to the referees*for*their helpful comments and useful suggestions on the earlier versions*of*this paper. ...##
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Skew Hadamard designs and their codes

2008
*
Designs, Codes and Cryptography
*

Quadratic Residues codes are obtained in the case

doi:10.1007/s10623-008-9173-y
fatcat:a2a5afytg5cxfdkcsc7guhr2da
*of*the Paley matrix. Results on the p−rank*of*skew Hadamard designs are rederived in that way. Codes from skew Hadamard designs are classified. ... Six new inequivalent [56, 28, 16] self-dual codes over GF (7) are obtained from skew Hadamard matrices*of*order 56, improving the only known quadratic double circulant code*of*length 56 over GF (7). ... The first author acknowledges partial support by a Project Completion Grant from the University*of*Louisville. ...##
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Preserving and Exploiting Genetic Diversity in Evolutionary Programming Algorithms

2009
*
IEEE Transactions on Evolutionary Computation
*

Evolution programming (EP) is an important category

doi:10.1109/tevc.2008.2011742
fatcat:utzr4ptt25ex7praq6gkeu76jm
*of*evolutionary algorithms. It relies primarily on mutation operators to search*for*solutions*of*function optimization problems (FOPs). ... Recently a series*of*new mutation operators have been proposed in order to improve the performance*of*EP. ... ., the number*of*distinct positions in the population): μ = 100;*2*) the number*of*rounds*of**tournaments*: q = √ μ = 10; 3) the initial standard deviation: η = 0.5; 4) the*exponent*parameter*of*the power-law ...##
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On a conjecture about the kth lower multiexponent

2010
*
Computers and Mathematics with Applications
*

Liu is proved to be true

doi:10.1016/j.camwa.2010.04.027
fatcat:x735rr4hwjfkzergcp2ta5us24
*for*the following cases: (1) k = n − i, where i =*2*, 3, 4, 5; (*2*) small n, where n ≤ 8; (3) the class*of**primitive*micro-symmetric digraphs*of*order n. ... Acknowledgements The authors would like to thank the referees*for*the valuable comments, and*for*the suggestions to improve the readability*of*this article. ... Then f (D n , k) = 1 + (2n − k −*2*) n − 1 k − n − 1 k*2*· k. By Lemma 2.1, D n is an*extremal*digraph reaching the*bound*given by f (n, k). ...
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