Abstract
A partial order of longstanding interest to mathematicians and chemists, the Young Diagram Lattice (YDL) is discussed in the context of complexity. Ruch’s (1975) identification of this partially ordered set with that appropriate to a general partial ordering for mixing is discussed. A mathematical quantity associated with each member of the set (the cardinality of maximal anti-chains for that member) is argued to provide a quantitative measure for complexity for members of the set. The measure has the desirable feature that low complexity is associated with both highly ordered and very random systems, while systems that have intermediate “structure” have larger complexity. Several quantitative examples based on the YDL are briefly discussed including statistical mechanics, diffusion, and biopolymeric complexity. Finally, a metaphor for complexity suggested by the YDL associates high complexity with posetic incomparability. Examples from sociology, ecology, and politics are discussed.
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© 2006 Springer-Verlag Berlin Heidelberg
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Seitz, W. (2006). Partial Orders and Complexity: The Young Diagram Lattice. In: Brüggemann, R., Carlsen, L. (eds) Partial Order in Environmental Sciences and Chemistry. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-33970-1_16
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DOI: https://doi.org/10.1007/3-540-33970-1_16
Publisher Name: Springer, Berlin, Heidelberg
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