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International Mathematics Research Notices Advance Access published online on October 9, 2009
International Mathematics Research Notices, doi:10.1093/imrn/rnp158
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© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

A Generalization of the Chebyshev Polynomials and Nonrooted Posets

Masaya Tomie

Institutes of Mathematics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan

Correspondence: Correspondence to be sent to: tomie{at}math.tsukuba.ac.jp

In this article we give a generalization of the Chebyshev polynomials of the first kind. Then we describe a Möbius function of the generalized subword order over Ps Formula . These results give the affirmative answer for the conjecture proposed in [A. Björner and B. Sagan, "Rationality of the Möbius function of the composition poset," Theoretical Computer Science 359, no. 1–3 (2006): 282–98.] and [B. Sagan and V. Vatter, "The Möbius function of the composition poset," Journal of Algebraic Combinatorics 24, no. 2 (2006): 117–36].

Communicated by Andrei Zelevinsky


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