New algorithms compute Hom spaces for poset representations in O(n^4 (thick(Y) + thick(Omega^1 Y))^2) time using a uniqueness result for lifts, plus a classical O(n^3 thick(Y)^3) method, both improving on O(n^6) and strengthening AIDA for multiparameter persistence.
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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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Computing Homomorphisms of Poset Representations with Applications to Multiparameter Persistence
New algorithms compute Hom spaces for poset representations in O(n^4 (thick(Y) + thick(Omega^1 Y))^2) time using a uniqueness result for lifts, plus a classical O(n^3 thick(Y)^3) method, both improving on O(n^6) and strengthening AIDA for multiparameter persistence.
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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.