The hakama without a crotch (skirt style as opposed to pantaloon style) is not necessarily a woman's style. It was formal wear, not riding breeches. I don't know when it was developed, but it keeps the lines of the kimono undisturbed. It is called an "andon bakama" - lantern hakama. Yes, the "b" is correct - that makes it easier to say following the "n" of the previous word.
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Ellis Amdur