On the Structure of the Bigrassmannian Permutation Poset
نویسندگان
چکیده
Let Sn and Bn denote the respective sets of ordinary and bigrassmannian permutations of order n, and let (Sn,≤) denote the Bruhat ordering permutation poset. We extensively study the structural properties of the restricted poset (Bn,≤), showing among other things that it is ranked, symmetric, and possesses the Sperner property. We also give formulae for the number of bigrassmannian permutations weakly below and weakly above a fixed bigrassmannian permutation, as well as the number of maximal chains.
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