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- W2950586469 abstract "We consider the zeta and Mobius functions of a partial order on integer compositions first studied by Bergeron, Bousquet-M'elou, and Dulucq. The Mobius function of this poset was determined by Sagan and Vatter. We prove rationality of various formal power series in noncommuting variables whose coefficients are evaluations of the zeta function and the Mobius function. The proofs are either directly from the definitions or by constructing finite-state automata. We also obtain explicit expressions for generating functions obtained by specializing the variables to commutative ones. We reprove Sagan and Vatter's formula for the Mobius function using this machinery. These results are closely related to those of Bjorner and Reutenauer about subword order, and we discuss a common generalization." @default.
- W2950586469 created "2019-06-27" @default.
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- W2950586469 date "2005-10-13" @default.
- W2950586469 modified "2023-09-28" @default.
- W2950586469 title "Rationality of the Mobius function of a composition poset" @default.
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