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A taste of nonstandard methods in combinatorics of numbers [article]

Mauro Di Nasso
2016 arXiv   pre-print
By presenting the proofs of a few sample results, we introduce the reader to the use of nonstandard analysis in aspects of combinatorics of numbers.  ...  Firstly, this paper is not to be taken as a comprehensive presentation of nonstandard methods in combinatorics, but only as a taste of that area of research.  ...  The goal of this paper is to give a soft introduction to the use of nonstandard methods in certain areas of density problems and Ramsey theory.  ... 
arXiv:1312.5059v2 fatcat:tpfqs7kbdngrbnjou2jcfzr3oi

A taste of nonstandard methods in combinatorics of numbers [chapter]

Mauro Di Nasso
2014 Geometry, Structure and Randomness in Combinatorics  
By presenting the proofs of a few sample results, we introduce the reader to the use of nonstandard analysis in aspects of combinatorics of numbers. 2000 Mathematics Subject Classification. 03H05; 11B05  ...  Two disclaimers are in order. Firstly, this paper is not to be taken as a comprehensive presentation of nonstandard methods in combinatorics, but only as a taste of that area of research.  ...  A nice introduction of nonstandard methods for number theorists, including a number of examples, is given in [15] (see also [12] ).  ... 
doi:10.1007/978-88-7642-525-7_3 fatcat:mjpeqfnnybcrtljg2piqv4y5ly

Page 4845 of Mathematical Reviews Vol. , Issue 89I [page]

1989 Mathematical Reviews  
There is very good taste displayed in the selection of problems. The solutions offered are elegant and clever.  ...  For example, the statement “if (Q,<) is a quasi-order (reflexive and transitive) and Q is the union of a countable number of finite sets then Q contains a countable incompatible set” is of the type mentioned  ... 

NONSTANDARD MODELS IN RECURSION THEORY AND REVERSE MATHEMATICS

C. T. CHONG, WEI LI, YUE YANG
2014 Bulletin of Symbolic Logic  
AbstractWe give a survey of the study of nonstandard models in recursion theory and reverse mathematics.  ...  We discuss the key notions and techniques in effective computability in nonstandard models, and their applications to problems concerning combinatorial principles in subsystems of second order arithmetic  ...  The blocking method in priority constructions (Mytilinaios [47] ) and the coding method in nonstandard models (Chong and Yang [14] ) were inspired by Shore's earlier works [53, 54] (as will be discussed  ... 
doi:10.1017/bsl.2014.14 fatcat:bijt7z5h2bgm3gnwbb45k76ctu

Mathematical Methods of Economics

Joel Franklin
1983 The American mathematical monthly  
finite number of linear inequalities in a finite number of unknowns, with a linear form to be minimized.  ...  This raises a question in combinatoric analysis: How may rational preferences orderings of m alternatives are there? The answer has appeared in [12] .  ... 
doi:10.1080/00029890.1983.11971202 fatcat:fgdryf3twjaffpzdampqtf2the

Mathematical Methods of Economics

Joel Franklin
1983 The American mathematical monthly  
finite number of linear inequalities in a finite number of unknowns, with a linear form to be minimized.  ...  This raises a question in combinatoric analysis: How may rational preferences orderings of m alternatives are there? The answer has appeared in [12] .  ... 
doi:10.2307/2975753 fatcat:hufqiumhhvgzvpxg66oufvftua

A combinatorial approach to the character theory of split metabelian groups

Andrew J Woldar
1989 Journal of combinatorial theory. Series A  
Our approach involves the theory of association schemes and provides yet another example of the applicability of this theory to problems in abstract algebra.  ...  An algorithm is developed for the computation of the character table of any split metabehan group.  ...  The reader is encouraged to attempt the algorithm for the symmetric group S3, the alternating group A,, and the dihedral groups D8 and Dz,, p an odd prime.  ... 
doi:10.1016/0097-3165(89)90008-3 fatcat:v2o6yesc6bb5fa5jxkq6p3etou

Pólya's Permanent Problem

William McCuaig
2004 Electronic Journal of Combinatorics  
A square real matrix is sign-nonsingular if it is forced to be nonsingular by its pattern of zero, negative, and positive entries.  ...  The structural characterizations, which are topological in nature, imply polynomial algorithms.  ...  The author wishes to thank Thomas Lundy for a helpful discussion, and Moshé Rosenfeld for suggesting that he look at a problem in which Victor Klee was interested.  ... 
doi:10.37236/1832 fatcat:uaqeso227fapvd6cnrvlcwnmhy

Invariant theory, Young bitableaux, and combinatorics

J Désarménien, Joseph P.S Kung, Gian-Carlo Rota
1978 Advances in Mathematics  
This is inefficient for practical computations, as the number of bitableaux introduced during a correction is, in general, very large.  ...  A(q)) be th e number of occurrences of xj (resp. z+) in the qth column of T (resp. T'). The C then [V, v'] is smuller than [T, T'] in the lexicographic order of their associated column sequences.  ...  AND ROTA geneous nonconstant invariant form of degree g. By Lemma C, m 3 d. We claim that the polynomial equals a polynomial in the brackets [xi, ,..., xid] .  ... 
doi:10.1016/0001-8708(78)90077-4 fatcat:akecu66s2bgbxnrywyff7cyxzq

Reviews and Descriptions of Tables and Books

1989 Mathematics of Computation  
It also presents a fairly large number of methods for convection-diffusion problems which are probably the most difficult ones in fluid simulation at high Reynolds number.  ...  A number of example programs are presented in the various chapters of the text.  ...  This is the proceedings of a symposium on the subject of the title of this volume. It consists of 22 papers by invited speakers. The papers presented were not subject to the refereeing process.  ... 
doi:10.1090/s0025-5718-89-99793-7 fatcat:kvef6ajuprc3hawasavgyp3uoi

Indexical order and the dialectics of sociolinguistic life

Michael Silverstein
2003 Language & Communication  
' deference-indexicality, speech levels, indexically significant variation in phonetics informed by a standard phonological register.  ...  We work through several classic examples of indexicality well-known in the literature of sociolinguistics, the clarification of which can be enhanced by using the concept of indexical order, viz., 'T/V  ...  An earlier version of this paper was invited as a Keynote Address to the 3rd Symposium about Language and Society Austin [SALSA III], April 1995. It appears in R.  ... 
doi:10.1016/s0271-5309(03)00013-2 fatcat:owrbqewvszdyveje3cnq5oyf4e

The Unreasonable Effectiveness of Mathematics

R. W. Hamming
1980 The American mathematical monthly  
His research interests are in numerical methods, software, simulation, and system performance and measurement.  ...  In a sense I am in the position of the early Greek philosophers who wondered about the material side, and my answers on the logical side are probably not much better than theirs were in their time.  ...  Finally there was artistic taste, which plays so large a role in modem mathematics. There are, of course, many different kinds of beauty in mathematics.  ... 
doi:10.2307/2321982 fatcat:dsqloirzvfexhm4ufismy4c3q4

The Unreasonable Effectiveness of Mathematics

R. W. Hamming
1980 The American mathematical monthly  
His research interests are in numerical methods, software, simulation, and system performance and measurement.  ...  In a sense I am in the position of the early Greek philosophers who wondered about the material side, and my answers on the logical side are probably not much better than theirs were in their time.  ...  Finally there was artistic taste, which plays so large a role in modem mathematics. There are, of course, many different kinds of beauty in mathematics.  ... 
doi:10.1080/00029890.1980.11994966 fatcat:735iyzou4rc2fgjg4po77hts3y

Uniform structures in the beginning of the third millenium

Hans-Peter A. Künzi
2007 Topology and its Applications  
It is the aim of the present survey article to discuss briefly results published by various researchers in the area of uniform structures over the past five years.  ...  Indeed a large number of new articles about fuzzy uniform structures appeared recently.  ...  In recent years balleans independently appeared in combinatorics [13] and in asymptotic topology (see, for instance, [48] ).  ... 
doi:10.1016/j.topol.2007.05.008 fatcat:fl7nlpaz5fa5rf2jpub7btva7a

Graph-based evolutionary algorithms

K.M. Bryden, D.A. Ashlock, S. Corns, S.J. Willson
2006 IEEE Transactions on Evolutionary Computation  
This use of graphs is a computationally inexpensive method of picking a global level of tradeoff between exploration and exploitation.  ...  He is a Researcher with interests in bioinformatics and the theory and practice of evolutionary computation. His doctoral work was in combinatorics.  ...  ACKNOWLEDGMENT The authors would like to thank the members of the Iowa State Complex Adaptive Systems Program for helpful comments and discussions.  ... 
doi:10.1109/tevc.2005.863128 fatcat:jibyyedwsranla2iw6nlchplae
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