Saturated chains in composition posets
نویسنده
چکیده
We study some poset structures on the set of all compositions. In the first case, the covering relation consists of inserting a part of size one to the left or to the right, or increasing the size of some part by one. The resulting poset N was studied by the author in [5] in relation to non-commutative term orders, and then in [6], where some results about generating functions for standard paths in N was established. This was inspired by the work of Bergeron, Bousquet-Mélou and Dulucq [1] on standard paths in the poset BBD, where there are additional cover relations which allows the insertion of a part of size one anywhere in the composition. Finally, following a suggestion by Richard Stanley we study a poset S which is an extension of BBD. This poset is related to quasi-symmetric functions. For these posets, we study generating functions for saturated chains of fixed width k. We also construct “labeled” non-commutative generating functions and their associated languages.
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