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We provide a direct proof of Agafonovs theorem which states that finite state selection preserves normality. We also extends this result to the more general setting of shifts of finite type by defining selections which are compatible the shift. A slightly more general statement is obtained as we show that any Markov measure is preserved by finite state compatible selection.
The commutative ambiguity of a context-free grammar G assigns to each Parikh vector v the number of distinct leftmost derivations yielding a word with Parikh vector v. Based on the results on the generalization of Newtons method to omega-continuous s
We give a short proof of a theorem of J.-E. Pin (theorem 1.1 below), which can be found in his thesis.
Parikhs theorem states that the Parikh image of a context-free language is semilinear or, equivalently, that every context-free language has the same Parikh image as some regular language. We present a very simple construction that, given a context-f
In two papers, Little and Sellers introduced an exciting new combinatorial method for proving partition identities which is not directly bijective. Instead, they consider various sets of weighted tilings of a $1 times infty$ board with squares and do
A finite form of de Finettis representation theorem is established using elementary information-theoretic tools: The distribution of the first $k$ random variables in an exchangeable binary vector of length $ngeq k$ is close to a mixture of product d