We revisit the Bose–Mesner algebra of the perfect matching association scheme. Our main results are
- An inductive algorithm, based on solving linear equations, to compute the eigenvalues of the orbital basis elements given the central characters of the symmetric groups.
- Universal formulas, as content evaluations of symmetric functions, for the eigenvalues of fixed orbitals.
- An inductive construction of an eigenvector (the so called first Gelfand–Tsetlin vector) in each eigenspace leading to a different inductive algorithm (not using central characters) for the eigenvalues of the orbital basis elements.
Revised: 2019-11-28
Accepted: 2019-11-29
Published online: 2020-06-02
Classification: 05E10, 05E05, 05E30
Keywords: perfect matching association scheme, content evaluation of symmetric functions, Gelfand–Tsetlin vectors.
@article{ALCO_2020__3_3_559_0, author = {Srinivasan, Murali K.}, title = {The perfect matching association scheme}, journal = {Algebraic Combinatorics}, pages = {559--591}, publisher = {MathOA foundation}, volume = {3}, number = {3}, year = {2020}, doi = {10.5802/alco.104}, language = {en}, url = {alco.centre-mersenne.org/item/ALCO_2020__3_3_559_0/} }
Srinivasan, Murali K. The perfect matching association scheme. Algebraic Combinatorics, Volume 3 (2020) no. 3, pp. 559-591. doi : 10.5802/alco.104. https://alco.centre-mersenne.org/item/ALCO_2020__3_3_559_0/
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