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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Relative Vorst theorem and relative Karoubi sequence yield improved injective stability bounds for relative K1 and K1Sp groups over regular rings.
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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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Improved injective stability for relative $\mathrm{K_1Sp}$-groups
Relative Vorst theorem and relative Karoubi sequence yield improved injective stability bounds for relative K1 and K1Sp groups over regular rings.