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Tiling Z with Triples Using Signed Permutation Matrices
Title
Tiling Z with Triples Using Signed Permutation Matrices.
Creator
Cattell, Liam J., Meyerowitz, Aaron, Florida Atlantic University
Abstract/Description
The topic of this paper is tiling the integers with triples, or more precisely to write Z as a disjoint union of translates of a given set of 3-subsets composed of basic shapes called prototiles. We fix the set of proto tiles P = { { 0, a, a+ v} , { U. b, a+ b}} and define an algorithm which returns a sequence of translates of P when given an initial subset of Z representing integers that are already tiled. This algorithm is then adapted to describe all possible tilings with triples from P...
Show moreThe topic of this paper is tiling the integers with triples, or more precisely to write Z as a disjoint union of translates of a given set of 3-subsets composed of basic shapes called prototiles. We fix the set of proto tiles P = { { 0, a, a+ v} , { U. b, a+ b}} and define an algorithm which returns a sequence of translates of P when given an initial subset of Z representing integers that are already tiled. This algorithm is then adapted to describe all possible tilings with triples from P using the action of certain signed permutation matrices on a subset of za+b , uamdy the 2" Yectors with all entries ±1. Given b > 2a, we research properties of the digraph of all possible tiling states and some related digraphs.
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Date Issued
2007
PURL
http://purl.flvc.org/fau/fd/FA00000732
Subject Headings
Tiling (Mathematics), Sequences (Mathematics), Permutation groups
Format
Document (PDF)
Investigations of a time dependent measurement technique for social judgment
Title
Investigations of a time dependent measurement technique for social judgment.
Creator
Kaufman, J., Florida Atlantic University, Vallacher, Robin R., Charles E. Schmidt College of Science, Department of Psychology
Abstract/Description
Argument is made for the use of variation permissive methods in the study of social judgment; one such dynamic method which purports to track on-line social evaluation (the mouse paradigm) is then introduced. The methodology of the mouse paradigm, which involves updating 'moment-to-moment' feelings via manipulation of a cursor by computer mouse, permits a wide range of experimental contrivance. Three varieties (SCALE, 1D and 2D), which differ in the amount of virtual (on screen) freedom of...
Show moreArgument is made for the use of variation permissive methods in the study of social judgment; one such dynamic method which purports to track on-line social evaluation (the mouse paradigm) is then introduced. The methodology of the mouse paradigm, which involves updating 'moment-to-moment' feelings via manipulation of a cursor by computer mouse, permits a wide range of experimental contrivance. Three varieties (SCALE, 1D and 2D), which differ in the amount of virtual (on screen) freedom of movement and psychological constraint, were tested with stereotyped targets (negative, ambivalent and positive) to determine any differences in their absolute distance time series and the extent to which aspects of these time series remained correlated with traditional scale-ratings of positivity and stability in feelings about targets. Results indicated a sharp difference between the two-dimensional (2D) variety and the one-dimensional varieties (SCALE and 1D), a finding which supports contention that the 2D variety possesses an appropriate balance of freedom and constraint.
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Date Issued
1994
PURL
http://purl.flvc.org/fcla/dt/15003
Subject Headings
Judgment, Attitude change, Verbal behavior, Psychometrics, Permutation groups, Group theory, Galois theory
Format
Document (PDF)
Low rank transitive representations, primitive extensions, and the collision problem in PSL (2, q)
Title
Low rank transitive representations, primitive extensions, and the collision problem in PSL (2, q).
Creator
Thapa Magar, Krishna B., Magliveras, Spyros S., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description
Every transitive permutation representation of a finite group is the representation of the group in its action on the cosets of a particular subgroup of the group. The group has a certain rank for each of these representations. We first find almost all rank-3 and rank-4 transitive representations of the projective special linear group P SL(2, q) where q = pm and p is an odd prime. We also determine the rank of P SL (2, p) in terms of p on the cosets of particular given subgroups. We then...
Show moreEvery transitive permutation representation of a finite group is the representation of the group in its action on the cosets of a particular subgroup of the group. The group has a certain rank for each of these representations. We first find almost all rank-3 and rank-4 transitive representations of the projective special linear group P SL(2, q) where q = pm and p is an odd prime. We also determine the rank of P SL (2, p) in terms of p on the cosets of particular given subgroups. We then investigate the construction of rank-3 transitive and primitive extensions of a simple group, such that the extension group formed is also simple. In the latter context we present a new, group theoretic construction of the famous Hoffman-Singleton graph as a rank-3 graph.
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Date Issued
2015
PURL
http://purl.flvc.org/fau/fd/FA00004471, http://purl.flvc.org/fau/fd/FA00004471
Subject Headings
Combinatorial designs and configurations, Cryptography, Data encryption (Computer science), Finite geometries, Finite groups, Group theory, Permutation groups
Format
Document (PDF)