Abstract
It is of interest to compare two partially ordered sets (more about this topic, see Chapter 10). We may, for example, ask whether all ≤ relations in one poset are reproduced in the other. In technical terms, we are asking whether or not
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References
Annoni, P. and Bruggemann, R. (2009). Exploring partial order of European countries. Soc. Indicators Res., 92, 471–487.
Annoni, P., Bruggemann, R. and Saltelli, A. (2011). Partial order investigation of multiple indicator systems using variance – based sensitivity analysis. Environ. Model. Softw., 26, 950–958.
Atkinson, M.D. and Chang, H.W. (1986). Extensions of partial orders of bounded width. Congressus Numerantium, 52, 21–35.
Borg, I. and Shye, S. (1995). Facet theory – form and content. Thousand Oaks, CA: Sage.
Bruggemann, R. and Fredrich, F. (1997). Eine mathematische Analyse der Fischgesellschaften im gosener Feuchtwiesengebiet. In IGB (Ed.), Berichte des IGB 4 (pp. 93–94). Berlin: IGB.
Bruggemann, R., Halfon, E., Welzl, G., Voigt, K. and Steinberg, C. (2001). Applying the concept of partially ordered sets on the ranking of near-shore sediments by a battery of tests. J. Chem. Inf. Comput. Sci., 41(4), 918–925.
Bruggemann, R., Welzl, G. and Voigt, K. (2003). Order theoretical tools for the evaluation of complex regional pollution patterns. J. Chem. Inf. Comput. Sci., 43, 1771–1779.
De Fraysseix, H. and De Mendez, P.O. (1996). Planarity and edge poset dimension. Eur. J. Combinatorics, 17, 731–740.
Edelman, P., Hibi, T. and Stanley, R.P. (1989). A recurrence for linear extensions. Order, 6, 15–18.
Kreimes, K. (1996). Oekologisches Wirkungskataster Baden-Wuerttemberg – Bewertung und zusammenfassende Darstellung von Untersuchungsergebnissen. In: U. Arndt, A. Fomin, and S. Lorenz (Eds.), Bio-indikation; neuere Entwicklungen – Nomenklatur – Synoekologische Aspekte; Beitraege und Diskussion 1. Hohenheimer Workshop zur Bioindikation am Kraftwerk Altbach-Deizisau, 1995 (pp. 160–169). Ostfildern: Guenter Heimbach.
Patil, G.P. (2005). Cross-disciplinary class room notes. Center for Statistical Ecology and Environmental Statistics, Penn State University.
Patil, G.P. and Taillie, C. (2004). Multiple indicators, partially ordered sets, and linear extensions: Multi-criterion ranking and prioritization. Environ. Ecol. Stat., 11, 199–228.
POSAC. See http://ca.huji.ac.il/bf/hudap
Stanley, R.P. (1986). Enumerative combinatorics volume I. Monterey: WadsworthandBrooks/Cole.
SYSTAT. http://www.systat.com/.
Trotter, W.T. (1992). Combinatorics and partially ordered sets dimension theory. Baltimore, MD: The Johns Hopkins University Press.
Voigt, K., Bruggemann, R. and Pudenz, S. (2004b). Chemical databases evaluated by order theoretical tools. Anal. Bioanal. Chem., 380, 467–474.
Voigt, K., Welzl, G. and Bruggemann, R. (2004a). Data analysis of environmental air pollutant monitoring systems in Europe. Environmetrics, 15, 577–596.
Winkler, P. (1982). Average height in a partially ordered set. Discr. Math., 39, 337–341.
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Brüggemann, R., Patil, G.P. (2011). Simple Combinatorial Structures. In: Ranking and Prioritization for Multi-indicator Systems. Environmental and Ecological Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8477-7_3
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