Séminaire Lotharingien de Combinatoire, 91B.49 (2024), 12 pp.
Christian Ikenmeyer and Greta Panova
All Kronecker Coefficients are Reduced Kronecker Coefficients
Abstract.
We settle the question of where exactly do the reduced Kronecker coefficients lie on the spectrum between the Littlewood-Richardson and Kronecker coefficients by
showing that every Kronecker coefficient of the symmetric group is equal to a reduced Kronecker coefficient by an explicit construction.
This implies the equivalence of a question by Stanley from 2000 and a question by Kirillov from 2004 about combinatorial interpretations of these two families of coefficients.
Moreover, as a corollary, we deduce that deciding the positivity of reduced Kronecker coefficients is NP-hard, and computing them is #P-hard under parsimonious many-one reductions.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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