We consider contact elements in the sutured Floer homology of solid tori with longitudinal sutures, as part of the (1+1)–dimensional topological quantum field theory defined by Honda, Kazez and Matic in [24]. The Z_2 SFH of these solid tori forms a "categorification of Pascal's triangle", and contact structures correspond bijectively to chord diagrams, or sets of disjoint properly embedded arcs in the disc. Their contact elements are distinct and form distinguished subsets of SFH of order given by the Narayana numbers. We find natural "creation and annihilation operators" which allow us to define a QFT–type basis of each SFH vector space, consisting of contact elements. Sutured Floer homology in this case reduces to the combinatorics of chord diagrams. We prove that contact elements are in bijective correspondence with comparable pairs of basis elements with respect to a certain partial order, and in a natural and explicit way. The algebraic and combinatorial structures in this description have intrinsic contact-topological meaning.
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