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.
Accepté le :
Publié le :
DOI : 10.4171/aihpd/113
Publié le :
DOI : 10.4171/aihpd/113
Classification :
05-XX, 81-XX
Mots-clés : Catalan numbers, chord diagrams, noncommutative QFT
Mots-clés : Catalan numbers, chord diagrams, noncommutative QFT
@article{AIHPD_2022__9_1_47_0, author = {de Jong, Jins and Hock, Alexander and Wulkenhaar, Raimar}, title = {Nested {Catalan} tables and a recurrence relation in noncommutative quantum field theory}, journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D}, pages = {47--72}, volume = {9}, number = {1}, year = {2022}, doi = {10.4171/aihpd/113}, mrnumber = {4407998}, zbl = {1495.81075}, language = {en}, url = {http://archive.numdam.org/articles/10.4171/aihpd/113/} }
TY - JOUR AU - de Jong, Jins AU - Hock, Alexander AU - Wulkenhaar, Raimar TI - Nested Catalan tables and a recurrence relation in noncommutative quantum field theory JO - Annales de l’Institut Henri Poincaré D PY - 2022 SP - 47 EP - 72 VL - 9 IS - 1 UR - http://archive.numdam.org/articles/10.4171/aihpd/113/ DO - 10.4171/aihpd/113 LA - en ID - AIHPD_2022__9_1_47_0 ER -
%0 Journal Article %A de Jong, Jins %A Hock, Alexander %A Wulkenhaar, Raimar %T Nested Catalan tables and a recurrence relation in noncommutative quantum field theory %J Annales de l’Institut Henri Poincaré D %D 2022 %P 47-72 %V 9 %N 1 %U http://archive.numdam.org/articles/10.4171/aihpd/113/ %R 10.4171/aihpd/113 %G en %F AIHPD_2022__9_1_47_0
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://archive.numdam.org/articles/10.4171/aihpd/113/
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