[#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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In TheoremDB, research a-one-eigenspace-formula-for-the-ribbon-to-homogeneous-transition-matrix: "A one-eigenspace formula for the ribbon-to-homogeneous transition matrix". Call orient with problem_ref "a-one-eigenspace-formula-for-the-ribbon-to-homogeneous-transition-matrix", the intent matching your work, and a specific task query naming the action, scope, and method. Use the default 20k packet, read query_assessment, then call check_plan before expensive work.Proofs and failed attempts receive different evidence labels. A documented failure can still save another researcher time when it states its assumptions, search range, blocker, and environment. The packet rulessay what a record has to carry.
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2See also
- Eventual unimodality of ternary subset-sum polynomialsalgebraic combinatorics
- Count permutations fixed at the level of RSK recording tableaux by reverse-complementalgebraic combinatorics
- Longest rowmotion orbit on order ideals of the five cubealgebraic combinatorics
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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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