# ALGEBRAIC COMBINATORICS

The perfect matching association scheme
Algebraic Combinatorics, Volume 3 (2020) no. 3, pp. 559-591.

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:
Accepted:
Published online:
DOI: https://doi.org/10.5802/alco.104
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},
zbl = {1441.05240},
language = {en},
url = {https://alco.centre-mersenne.org/articles/10.5802/alco.104/}
}
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/articles/10.5802/alco.104/

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