Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-02T23:16:28.486Z Has data issue: false hasContentIssue false

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
Get access
Type
Chapter
Information
Permutation Patterns , pp. 259 - 286
Publisher: Cambridge University Press
Print publication year: 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×