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Permutations with k-regular descent patterns

Published online by Cambridge University Press:  05 October 2010

Anthony Mendes
Affiliation:
Department of Mathematics Cal Poly State University San Luis Obispo, CA 93407
Jeffrey B. Remmel
Affiliation:
Department of Mathematics University of California, San Diego La Jolla, CA 92093
Amanda Riehl
Affiliation:
Department of Mathematics University of Wisconsin Eau Claire, Eau Claire, WI 54702
Steve Linton
Affiliation:
University of St Andrews, Scotland
Nik Ruškuc
Affiliation:
University of St Andrews, Scotland
Vincent Vatter
Affiliation:
Dartmouth College, New Hampshire
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Permutation Patterns , pp. 259 - 286
Publisher: Cambridge University Press
Print publication year: 2010

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References

[1] D., André. Développements de sec x et de tang x. C. R. Math. Acad. Sci. Paris, 88:965–967, 1879.Google Scholar
[2] D., André. Sur les permutations alternées. J. Math. Pures Appl., 7:167–184, 1881.Google Scholar
[3] G. E., Andrews and D., Foata. Congruences for the q-secant numbers. European J. Combin., 1(4):283–287, 1980.Google Scholar
[4] G. E., Andrews and I., Gessel. Divisibility properties of the q-tangent numbers. Proc. Amer. Math. Soc., 68(3):380–384, 1978.Google Scholar
[5] F., Brenti. Permutation enumeration symmetric functions, and unimodality. Pacific J. Math., 157(1):1–28, 1993.Google Scholar
[6] L., Carlitz. The coefficients of cosh x/cos x. Monatsh. Math., 69:129–135, 1965.Google Scholar
[7] L., Carlitz. Sequences and inversions. Duke Math. J., 37:193–198, 1970.Google Scholar
[8] Ö., Eğecioğlu and J. B., Remmel. Brick tabloids and the connection matrices between bases of symmetric functions. Discrete Appl. Math., 34(1-3):107–120, 1991.Google Scholar
[9] J.-M., Fédou and D., Rawlings. Statistics on pairs of permutations. Discrete Math., 143(1-3):31–45, 1995.Google Scholar
[10] D., Foata. Further divisibility properties of the q-tangent numbers. Proc. Amer. Math. Soc., 81(1):143–148, 1981.Google Scholar
[11] I. M., Gessel. Some congruences for generalized Euler numbers. Canad. J. Math., 35(4):687–709, 1983.Google Scholar
[12] V. J. W., Guo and J., Zeng. Some arithmetic properties of the q-Euler numbers and q-Salié numbers. European J. Combin., 27(6):884–895, 2006.Google Scholar
[13] T. M., Langley and J. B., Remmel. Enumeration of m-tuples of permutations and a new class of power bases for the space of symmetric functions. Adv. in Appl. Math., 36(1):30–66, 2006.Google Scholar
[14] D. J., Leeming and R. A., MacLeod. Some properties of generalized Euler numbers. Canad. J. Math., 33(3):606–617, 1981.Google Scholar
[15] I. G., Macdonald. Symmetric functions and Hall polynomials. Oxford Mathematical Monographs. The Clarendon Press Oxford University Press, New York, second edition, 1995.Google Scholar
[16] A., Mendes. Building generating functions brick by brick. PhD thesis, University of California, San Diego, 2004.
[17] A., Mendes and J. B., Remmel. Generating functions for statistics on Ck ≀ Sn. Sém. Lothar. Combin., 54A:Art. B54At, 40 pp., 2005/07.Google Scholar
[18] A., Mendes and J. B., Remmel. Permutations and words counted by consecutive patterns. Adv. in Appl. Math., 37(4):443–480, 2006.Google Scholar
[19] H., Prodinger. Combinatorics of geometrically distributed random variables: new q-tangent and q-secant numbers. Int. J. Math. Math. Sci., 24(12):825–838, 2000.Google Scholar
[20] H., Prodinger. q-enumeration of Salié permutations. Ann. Comb., 11(2):213–225, 2007.Google Scholar
[21] J. B., Remmel and A., Riehl. Generating functions for permutations which contain a given descent set. Electron. J. Combin., 17(1):Research Paper 27, 33 pp., 2010.Google Scholar
[22] B. E., Sagan and P., Zhang. Arithmetic properties of generalized Euler numbers. Southeast Asian Bull. Math., 21(1):73–78, 1997.Google Scholar
[23] R. P., Stanley. Binomial posets, Möbius inversion, and permutation enumeration. J. Combinatorial Theory Ser. A, 20(3):336–356, 1976.Google Scholar
[24] R. P., Stanley. Enumerative combinatorics. Vol. 1, volume 49 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 1997.Google Scholar
[25] J. D., Wagner. The permutation enumeration of wreath products Ck ≀ Sn of cyclic and symmetric groups. Adv. in Appl. Math., 30(1-2):343–368, 2003.Google Scholar

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