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All continuous endomorphisms f ∞ of the shift dynamical system S on the 2-adic integers Z 2 are induced by some f : B n → {0, 1}, where n is a positive integer, B n is the set of n-blocks over {0, 1}, and f ∞ (x) = y 0 y 1 y 2. .. We prove that D, V • D, S, and V • S are conjugate to S and are the only continuous endomorphisms of S whose parity vector(More)
Given a partition λ of n, a k-minor of λ is a partition of n − k whose Young diagram fits inside that of λ. We find an explicit function g(n) such that any partition of n can be reconstructed from its set of k-minors if and only if k ≤ g(n). In particular, partitions of n ≥ k 2 + 2k are uniquely determined by their sets of k-minors. This result completely(More)
The 3x + 1 Conjecture asserts that the T-orbit of every positive integer contains 1, where T maps x → x/2 for x even and x → (3x + 1)/2 for x odd. A set S of positive integers is sufficient if the orbit of each positive integer intersects the orbit of some member of S. In [9] it was shown that every arithmetic sequence is sufficient. In this paper we(More)
Let A be a finite alphabet and let L ⊂ (A *) n be an n-variable language over A. We say that L is regular if it is the language accepted by a synchronous n-tape finite state automaton, it is quasi-regular if it is accepted by an asynchronous n-tape automaton, and it is weakly regular if it is accepted by a non-deterministic asynchronous n-tape automaton. We(More)
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