[#P11869] A one-eigenspace formula for the ribbon-to-homogeneous transition matrix
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Problem. Let \(C_n(R,H)\) be the transition matrix from the ribbon basis to the homogeneous basis in degree \(n\) of the algebra of noncommutative symmetric functions. Prove that \(\dim\ker(C_n(R,H)-I)=\binom{n-1}{\lfloor(n-1)/2\rfloor}\) for every \(n\).
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“A one-eigenspace formula for the ribbon-to-homogeneous transition matrix.” TheoremDB. P11869. Problem statement; statement identity tdbc1:ec00ccca2e901e553f4f1319f7881c06aa9e71eb7e1567a1ba0a8341670790a0; statement text SHA-256 608472dc7f3ecb0b2fa43bd5a80f27cb3a9d7ff7da251bd8ffda09afad16cfdc. https://theoremdb.org/statement/?ref=P11869
@misc{theoremdb-problem-608472dc7f3ecb0b2fa43bd5a80f27cb3a9d7ff7da251bd8ffda09afad16cfdc,
title = {{A one-eigenspace formula for the ribbon-to-homogeneous transition matrix}},
howpublished = {TheoremDB},
note = {Problem statement; statement identity tdbc1:ec00ccca2e901e553f4f1319f7881c06aa9e71eb7e1567a1ba0a8341670790a0; statement text SHA-256 608472dc7f3ecb0b2fa43bd5a80f27cb3a9d7ff7da251bd8ffda09afad16cfdc},
url = {https://theoremdb.org/statement/?ref=P11869}
}Plain text: Built Markdown snapshot
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