참고문헌
- R. Askey and M. E. H. Ismail, Permutation problems and special functions, Canad. J. Math. 28 (1976), no. 4, 853-874. https://doi.org/10.4153/CJM-1976-082-8
- R. Chapman and L. K. Williams, A conjecture of Stanley on alternating permutations, Electron. J. Combin. 14 (2007), no. 1, Note 16, 7 pp.
- N. Eriksen, R. Freij, and J. Wastlund, Enumeration of derangements with descents in prescribed positions, Electron. J. Combin. 16 (2009), #R32.
- D. Foata and D. Zeilberger, Laguerre polynomials, weighted derangements, and positivity, SIAM J. Discrete Math. 1 (1988), no. 4, 425-433. https://doi.org/10.1137/0401043
- I. M. Gessel and C. Reutenauer, Counting permutations with given cycle structure and descent set, J. Combin. Theory Ser. A 64 (1993), no. 2, 189-215. https://doi.org/10.1016/0097-3165(93)90095-P
- G.-N. Han and G. Xin, Permutations with extremal number of fixed points, J. Combin. Theory Ser. A 116 (2009), no. 2, 449-459. https://doi.org/10.1016/j.jcta.2008.08.001
- D. Kim and J. Zeng, A new decomposition of derangements, J. Combin. Theory Ser. A 96 (2001), no. 1, 192-198. https://doi.org/10.1006/jcta.2001.3190
- R. P. Stanley, Enumerative Combinatorics. Vol. 2, volume 62 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, 1999.
- R. P. Stanley, Alternating permutations and symmetric functions, J. Combin. Theory Ser. A 114 (2007), no. 3, 436-460. https://doi.org/10.1016/j.jcta.2006.06.008
- R. P. Stanley, A survey of alternating permutations, In Combinatorics and graphs, volume 531 of Contemp. Math., pages 165-196. Amer. Math. Soc., Providence, RI, 2010.
- R. P. Stanley, Enumerative Combinatorics. Vol. 1, Second ed., Cambridge University Press, New York/Cambridge, 2011.
- J. Steinhardt, Permutations with ascending and descending blocks, Electron. J. Combin. 17 (2010), #R14.
- J. Zeng, Linearisation de produits de polynomes de Meixner, Krawtchouk, et Charlier., SIAM J. Math. Anal. 21 (1990), no. 5, 1349-1368. https://doi.org/10.1137/0521075
- J. Zeng, Weighted derangements and the linearization coefficients of orthogonal Sheffer polynomials, Proc. London Math. Soc. (3) 65 (1992), no. 1, 1-22.