Avoiding 2-letter signed patterns

الأصل · EN

Let Bₙ be the hyperoctahedral group; that is, the set of all signed permutations on n letters, and let Bₙ(T) be the set of all signed permutations in Bₙ which avoids a set T of signed patterns. In this paper, we find all the cardinalities of the sets Bₙ(T) where T B₂. This allow us to express these cardinalities via inverse of binomial coefficients, binomial coefficients, Catalan numbers, and Fibonacci numbers.