Geodesic
Nested Catalan tables and a recurrence relation in noncommutative quantum field theory
Annales de l’Institut Henri Poincaré D, Tome 9 (2022) no. 1, pp. 47-72.

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Correlation functions in a dynamic quartic matrix model are obtained from the twopoint function through a recurrence relation. This paper gives the explicit solution of the recurrence by mapping it bijectively to a two-fold nested combinatorial structure each counted by Catalan numbers. These “nested Catalan tables” have a description as diagrams of non-crossing chords and threads.

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DOI : 10.4171/aihpd/113
Classification : 05-XX, 81-XX
Keywords: Catalan numbers, chord diagrams, noncommutative QFT 
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     title = {Nested {Catalan} tables and a recurrence relation in noncommutative quantum field theory},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
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de Jong, Jins; Hock, Alexander; Wulkenhaar, Raimar. Nested Catalan tables and a recurrence relation in noncommutative quantum field theory. Annales de l’Institut Henri Poincaré D, Tome 9 (2022) no. 1, pp. 47-72. doi : 10.4171/aihpd/113. http://geodesic.mathdoc.fr/articles/10.4171/aihpd/113/

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