Media theory: Representations and examples

In this paper we develop a representational approach to media theory. We construct representations of media by well-graded families of sets and partial cubes and establish the uniqueness of these representations. Two particular examples of media are also described in detail.

[1]  M. Deza,et al.  Mosaics and their isometric embeddings , 2002 .

[2]  David Eppstein,et al.  Algorithms for media , 2002, Discret. Appl. Math..

[3]  Leonard M. Blumenthal,et al.  Theory and applications of distance geometry , 1954 .

[4]  Bernd Sturmfels,et al.  Oriented Matroids: A Second Orientation Session , 1999 .

[5]  Sergei Ovchinnikov,et al.  Advances in media theory , 2000 .

[6]  Jim Lawrence,et al.  Oriented matroids , 1978, J. Comb. Theory B.

[7]  Günter M. Ziegler,et al.  Oriented Matroids , 2017, Handbook of Discrete and Computational Geometry, 2nd Ed..

[8]  Jean-Paul Doignon,et al.  Stochastic evolution of rationality , 1997 .

[9]  S. Ovchinnikov.  Convexity in subsets of lattices. , 1980 .

[10]  Fa Dick,et al.  Algebraic theory of Penrose's non-periodic tilings of the plane. I, II : dedicated to G. Pólya , 1981 .

[11]  Michel Deza,et al.  Geometry of cuts and metrics , 2009, Algorithms and combinatorics.

[12]  R. Duncan Luce,et al.  Choice, Decision, and Measurement: Essays in Honor of R. Duncan Luce , 1997 .

[13]  K. Bogart.  Preference structures I: Distances between transitive preference relations† , 1973 .

[14]  B. Grofman,et al.  A stochastic model of preference change and its application to 1992 presidential election panel data , 1999 .

[15]  N. D. Bruijn.  Algebraic theory of Penrose''s non-periodic tilings , 1981 .

[16]  Stan Wagon.  Mathematica in action , 1991 .

[17]  D. Djoković.  Distance-preserving subgraphs of hypercubes , 1973 .

[18]  Falmagne.  Stochastic Token Theory , 1997, Journal of mathematical psychology.

[19]  J. Falmagne.  A stochastic theory for the emergence and the evolution of preference relations , 1996 .

[20]  M. Senechal.  Quasicrystals and geometry , 1995 .

[21]  Sergei Ovchinnikov,et al.  Convex geometry and group choice , 1983 .

[22]  Eckhard Meinrenken,et al.  LIE GROUPS AND LIE ALGEBRAS , 2021, Lie Groups, Lie Algebras, and Cohomology. (MN-34), Volume 34.

[23]  Jean-Claude Falmagne,et al.  Well-graded families of relations , 1997, Discret. Math..

[24]  Arcwise Isometries,et al.  A Course in Metric Geometry , 2001 .

[25]  G. C. Shephard,et al.  Tilings and Patterns , 1990 .

[26]  Sergei Ovchinnikov,et al.  Media theory , 2002, Discret. Appl. Math..