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\bibitem{bh:dmf}
{\sc Babson, E., and Hersh, P.}
\newblock Discrete {M}orse functions from lexicographic orders.
\newblock {\em Trans. Amer. Math. Soc. 357}, 2 (2005), 509--534 (electronic).

\bibitem{bbd:spc}
{\sc Bergeron, F., Bousquet-M{\'e}lou, M., and Dulucq, S.}
\newblock Standard paths in the composition poset.
\newblock {\em Ann. Sci. Math. Qu\'ebec 19}, 2 (1995), 139--151.

\bibitem{bjo:scp}
{\sc Bj{\"o}rner, A.}
\newblock Shellable and {C}ohen-{M}acaulay partially ordered sets.
\newblock {\em Trans. Amer. Math. Soc. 260}, 1 (1980), 159--183.

\bibitem{bjo:mfs}
{\sc Bj{\"o}rner, A.}
\newblock The {M}\"obius function of subword order.
\newblock In {\em Invariant theory and tableaux (Minneapolis, MN, 1988)},
  vol.~19 of {\em IMA Vol. Math. Appl.} Springer, New York, 1990, pp.~118--124.

\bibitem{bjo:mff}
{\sc Bj{\"o}rner, A.}
\newblock The {M}\"obius function of factor order.
\newblock {\em Theoret. Comput. Sci. 117}, 1-2 (1993), 91--98.

\bibitem{br:rmf}
{\sc Bj{\"o}rner, A., and Reutenauer, C.}
\newblock Rationality of the {M}\"obius function of subword order.
\newblock {\em Theoret. Comput. Sci. 98}, 1 (1992), 53--63.
\newblock Second Workshop on Algebraic and Computer-theoretic Aspects of Formal
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\bibitem{bs:rmf}
{\sc Bj{\"o}rner, A., and Sagan, B.}
\newblock Rationality of the {M}\"obius function of the composition poset.
\newblock In preparation.

\bibitem{bs:ayl}
{\sc Bj{\"o}rner, A., and Stanley, R.~P.}
\newblock An analogue of {Y}oung's lattice for compositions.
\newblock \href{http://arxiv.org/abs/math.CO/0508043}
  {\texttt{arXiv:math.CO/0508043}}.

\bibitem{bw:boc}
{\sc Bj{\"o}rner, A., and Wachs, M.}
\newblock Bruhat order of {C}oxeter groups and shellability.
\newblock {\em Adv. in Math. 43}, 1 (1982), 87--100.

\bibitem{bon:cp}
{\sc B{\'o}na, M.}
\newblock {\em Combinatorics of permutations}.
\newblock Discrete Mathematics and its Applications (Boca Raton). Chapman \&
  Hall/CRC, Boca Raton, FL, 2004.

\bibitem{cw:fsc}
{\sc Chow, T., and West, J.}
\newblock Forbidden subsequences and {C}hebyshev polynomials.
\newblock {\em Discrete Math. 204}, 1-3 (1999), 119--128.

\bibitem{er:ttf}
{\sc Ehrenborg, R., and Readdy, M.}
\newblock The {T}chebyshev transforms of the first and second kinds.
\newblock \href{http://arxiv.org/abs/math.CO/0412124}
  {\texttt{arXiv:math.CO/0412124}}.

\bibitem{far:chp}
{\sc Farmer, F.~D.}
\newblock Cellular homology for posets.
\newblock {\em Math. Japon. 23}, 6 (1978/79), 607--613.

\bibitem{for:dmt}
{\sc Forman, R.}
\newblock A discrete {M}orse theory for cell complexes.
\newblock In {\em Geometry, topology, \& physics}, Conf. Proc. Lecture Notes
  Geom. Topology, IV. Internat. Press, Cambridge, MA, 1995, pp.~112--125.

\bibitem{for:mtc}
{\sc Forman, R.}
\newblock Morse theory for cell complexes.
\newblock {\em Adv. Math. 134}, 1 (1998), 90--145.

\bibitem{her:odf}
{\sc Hersh, P.}
\newblock On optimizing discrete {M}orse functions.
\newblock \href{http://arxiv.org/abs/math.CO/0311270}
  {\texttt{arXiv:math.CO/0311270}}.

\bibitem{het:tp}
{\sc Hetyei, G.}
\newblock Tchebyshev posets.
\newblock {\em Discrete Comput. Geom. 32}, 4 (2004), 493--520.

\bibitem{kru:twq}
{\sc Kruskal, J.~B.}
\newblock The theory of well-quasi-ordering: {A} frequently discovered concept.
\newblock {\em J. Combinatorial Theory Ser. A 13\/} (1972), 297--305.

\bibitem{mv:rpc}
{\sc Mansour, T., and Vainshtein, A.}
\newblock Restricted permutations, continued fractions, and {C}hebyshev
  polynomials.
\newblock {\em Electron. J. Combin. 7\/} (2000), Research Paper 17, 9 pp.
  (electronic).

\bibitem{rot:tmf}
{\sc Rota, G.-C.}
\newblock On the foundations of combinatorial theory. {I}. {T}heory of
  {M}\"obius functions.
\newblock {\em Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 2\/} (1964),
  340--368 (1964).

\bibitem{sne:scc}
{\sc Snellman, J.}
\newblock Saturated chains in composition posets.
\newblock \href{http://arxiv.org/abs/math.CO/0505262}
  {\texttt{arXiv:math.CO/0505262}}.

\bibitem{sne:spa}
{\sc Snellman, J.}
\newblock Standard paths in another composition poset.
\newblock {\em Electron. J. Combin. 11}, 1 (2004), Research Paper 76, 8 pp.
  (electronic).

\bibitem{sta:ec1}
{\sc Stanley, R.~P.}
\newblock {\em Enumerative combinatorics. {V}ol. 1}, vol.~49 of {\em Cambridge
  Studies in Advanced Mathematics}.
\newblock Cambridge University Press, Cambridge, 1997.
\newblock With a foreword by Gian-Carlo Rota, Corrected reprint of the 1986
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\bibitem{vie:mcs}
{\sc Viennot, G.}
\newblock Maximal chains of subwords and up-down sequences of permutations.
\newblock {\em J. Combin. Theory Ser. A 34}, 1 (1983), 1--14.

\bibitem{wm:gcp}
{\sc Wang, T.~M., and Ma, X.~R.}
\newblock A generalization of the {C}ohen-{M}acaulay property of the {M}\"obius
  function of a word poset.
\newblock {\em Acta Math. Appl. Sinica 20}, 3 (1997), 431--437.

\bibitem{war:mfs}
{\sc Warnke, I.}
\newblock The {M}\"obius-function of subword orders.
\newblock {\em Rostock. Math. Kolloq.}, 46 (1993), 25--31.

\bibitem{wil:pp}
{\sc Wilf, H.~S.}
\newblock The patterns of permutations.
\newblock {\em Discrete Math. 257}, 2-3 (2002), 575--583.

\end{thebibliography}