Annals of Combinatorics 7(2003) 1-14Words Restricted by 3-Letter Generalized Multipermutation Patterns Alexander Burstein and Toufik Mansour Department of Mathematics, Iowa State University, Ames, IA
50011-2064, USA Department of Mathematics, Chalmers Univeristy of Technology, 412~96 GÖteborg,
Sweden Received November 20, 2002 AMS Subject Classification: 05A05, 05A15 Abstract. We find exact formulas and/or generating functions for the number of words avoiding 3-letter generalized multipermutation patterns and find which of them are equally avoided. Keywords: k-ary words, generalized patterns, generating functions References 1. E. Babson and E. Steingrímsson, Generalized permutation patterns and a classification of the Mahonian statistics, Sém. Lothar. Combin. B44b (2000) 18 pp. 2. A. Burstein, Enumeration of words with forbidden patterns, Ph.D. Thesis, University of Pennsylvania, 1998. 3. A. Burstein and T.Mansour, Words restricted by patterns with at most 2 distinct letters, Elect. J. Combin. 9 (2) (2002) #R3. 4. A. Claesson, Generalized pattern avoidance, Europ. J. Combin. 22 (2001) 961–971. 5. A. Claesson and T. Mansour, Enumerating permutations avoiding a pair of Babson- Steingrímsson patterns, preprint, math.CO/0107044. 6. D.E. Knuth, The Art of Computer Programming, Vols. 1 and 3, Addison-Wesley, NY, 1968, 1973. 7. A.M. Odlyzko, Asymptotic enumeration methods, In: Handbook of Combinatorics, Vol. 2, R.L. Graham, M. Grötchel and L. Lovász, Eds., MIT Press, 1995, pp. 1063–1230. 8. R. Simion and F.W. Schmidt, Restricted permutations, Europ. J. of Combin. 6 (1985) 383– 406. 9. D. Zeilberger, Enumeration schemes, and more importantly, their automatic generation, Ann. Combin. 2 (1998) 185–195. |