Defines occupation ideals from Parikh monomials of trajectories in directed support graphs of Markov chains to encode distinct occupation patterns and separate reachability, trajectory, and occupation-pattern growth.
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2026 2verdicts
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The Holte matrix has biorthogonal eigenvectors expressed via Stirling numbers, Eulerian polynomials, and symmetric quotient polynomials, with cascade-free avoidance counts being Chebyshev polynomials exactly for k=3 but not for k>=4.
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Occupation Ideals and Parikh Images in Markov Support Dynamics
Defines occupation ideals from Parikh monomials of trajectories in directed support graphs of Markov chains to encode distinct occupation patterns and separate reachability, trajectory, and occupation-pattern growth.
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Biorthogonal eigenvectors of the Holte carry matrix and cascade-free enumeration
The Holte matrix has biorthogonal eigenvectors expressed via Stirling numbers, Eulerian polynomials, and symmetric quotient polynomials, with cascade-free avoidance counts being Chebyshev polynomials exactly for k=3 but not for k>=4.