Geodesic
Jucys-Murphy elements and a presentation for partition algebras
Journal of Algebraic Combinatorics, Tome 37 (2013) no. 3, pp. 401-454.

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Summary: We give a new presentation for the partition algebras. This presentation was discovered in the course of establishing an inductive formula for the partition algebra Jucys-Murphy elements defined by Halverson and Ram (Eur. J. Comb. 26:869-921, 2005). Using Schur-Weyl duality we show that our recursive formula and the original definition of Jucys-Murphy elements given by Halverson and Ram are equivalent. The new presentation and inductive formula for the partition algebra Jucys-Murphy elements given in this paper are used to construct the seminormal representations for the partition algebras in a separate paper.
Keywords: partition algebras, jucys-murphy elements, central elements, presentation 
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Enyang, John. Jucys-Murphy elements and a presentation for partition algebras. Journal of Algebraic Combinatorics, Tome 37 (2013) no. 3, pp. 401-454. http://geodesic.mathdoc.fr/item/JAC_2013__37_3_a5/