We know from Littlewood (1968) that the moments of order 4 of the classical Rudin–Shapiro polynomials Pn(z) satisfy a linear recurrence of degree 2. In a previous article, we developed a new approach, which enables us to compute exactly all the moments Mq(Pn) of even order q for q 32. We were also able to check a conjecture on the asymptotic behavior of Mq(Pn), namely Mq(Pn) ∼ Cq2, where Cq = 2...

We give the Heisenberg realization for the quantum algebra Uq(sln), which is written by the q-difference operator on the flag manifold. We construct it from the action of Uq(sln) on the q-symmetric algebra Aq(Matn) by the Borel-Weil like approach. Our realization is applicable to the construction of the free field realization for the Uq(ŝln) [AOS].

A result of Nicaud states that the number of distinct unary regular string languages recognized by minimal deterministic finite automata (DFAs) with n states is asymptotically equal to n2n−1. We consider the analogous question for symmetric difference automata (Z2NFAs), and show that precisely 22n−1 unary languages are recognized by n-state minimal Z2-NFAs.

Recently, a characterization of the class of nondeterministic finite automata (NFAs) for which determinization results in a minimal deterministic finite automaton (DFA), was given in [2]. We present a similar result for the case of symmetric difference NFAs. Also, we show that determinization of any minimal symmetric difference NFA produces a minimal DFA.