WORK IN PROGRESS!!! \section{Introductory notes on partition categories} \subsection{Some references} The partition category appears implicitly in
[M91] P. Martin, Potts models and related problems in statistical mechanics, World Scientific 1991
and more explicitly in
[M94] P. Martin. Temperley-Lieb algebras for non-planar statistical mechanics - the partition algebra construction, JKTR 3 (1994), 51-82. (Yale CTP 1992 preprint: YCTP-P34-92.)
A more recent reference/review is:
[M08] P. P. Martin. On diagram categories, representation theory and Statistical Mechanics, AMS Contemporary Math 456 (2008) 99-136.

Other papers on the partition algebras include:
[MS93] P. P. Martin and H. Saleur, On an algebraic approach to higher dimensional statistical mechanics, Comm Math Phys 158 (1993) 155-190. (YCTP-P33-92)
[MS94] P. P. Martin and H. Saleur. Algebras in higher dimensional statistical mechanics - the exceptional partition algebras, Lett Math Phys 30 (1994), 179-185. (arXiv:hep-th/9302095v1)
[J94] V.F.R. Jones, in Subfactors ed. H. Araki, World Scientific 1994.
[MW98] P. P. Martin and D. Woodcock, The partition algebras and a new deformation of the Schur algebras, J Algebra 203 (1998) 91-124.
[DW] W.F. Doran and D.B. Wales, The partition algebra revisited, J Alg .
[HR05] T. Halverson and A. Ram, Partition algebras, Euro J Combin 26 (2005) 869-921.
[E10] J. Enyang, Jucys-Murphy elements and a presentation for partition algebras, http://arxiv.org/abs/1009.1939.
... more to follow.

Wider related refs:
[Baxter] R J Baxter,
[Brauer] Brauer,
[Yang67] C.N. Yang, Some exact results for the many-body problem ..., Phys Rev Lett 19 (1967) 1312-1315.
[Zamolodchikov79] A B and Al B Zamolodchikov, Factorised S-matrices ..., Annals of Phys 120 (1979) 253.

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