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- W1954240747 abstract "We generalize the combinatorial framework of free monoids to what we call a network, which allows us to count words in a free monoid on an alphabet $A$ corresponding to walks between specified vertices in a digraph where each arc is assigned a subset of $A$. Our main result is a generalization of a theorem of Gessel to the monoid network setting, and we use it to complete the enumeration of permutations with parity restrictions on peaks and valleys, and to give a systematic method for obtaining generating functions for permutation statistics that can be characterized in terms of increasing runs." @default.
- W1954240747 created "2016-06-24" @default.
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- W1954240747 date "2015-05-09" @default.
- W1954240747 modified "2023-09-27" @default.
- W1954240747 title "Monoid networks and counting permutations by runs" @default.
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