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Permutations of a multiset avoiding permutations of length 3. (English) Zbl 0988.05005
A sequence of numbers $$\alpha =(a_{1},\dots ,a_{m})$$ is contained in a sequence of numbers $$\beta =(b_{1},\dots ,b_{n})$$ if there is a subsequence $$(b_{i_{1}},\dots,b_{i_{m}})$$, $$i_{1}<\dots <i_{m},$$ so that $$a_{s}\leq a_{t}$$ iff $$b_{i_{s}}\leq b_{i_{t}}.$$ In the paper the permutations of a multiset which do not contain certain subsequences of length $$3$$ are considered, in many cases an enumeration of such permutations is given.

##### MSC:
 05A05 Permutations, words, matrices 05A15 Exact enumeration problems, generating functions
##### Keywords:
forbidden; permutation; multiset; enumeration
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##### References:
 [1] Atkinson, M.D.; Walker, L.; Linton, S.A., Priority queues and multi-sets, Electron. J. comb., 2, Paper R24 (18 pp.), (1995) [2] Atkinson, M.D., Generalised stack permutations, Comb. probab. comput., 7, 239-246, (1998) · Zbl 0917.05005 [3] Atkinson, M.D., Permutations which are the union of an increasing and a decreasing sequence, Electron. J. comb., 5, Paper R6 (13 pp.), (1998) · Zbl 0885.05011 [4] Bóna, M., Exact enumeration of 1342-avoiding permutations; a close link with labeled trees and planar maps, J. comb. theory, series A, 80, 257-272, (1997) · Zbl 0887.05004 [5] Bóna, M., The permutations classes equinumerous to the smooth class, Electron. J. comb., 5, Paper R31 (12 pp.), (1998) [6] A. Burstein, 1998 [7] Even, S.; Itai, A., Queues, stacks and graphs, (), 71-86 [8] Pratt, V.R., Computing permutations with double-ended queues, parallel stacks and parallel queues, Proc. ACM symp. theory comput., 5, 268-277, (1973) [9] Shapiro, L.; Stephens, A.B., Bootstrap percolation, the Schröder number, and the N -kings problem, SIAM J. discrete math., 2, 275-280, (1991) · Zbl 0736.05008 [10] Simion, R.; Schmidt, F.W., Restricted permutations, Europ. J. combinatorics, 6, 383-406, (1985) · Zbl 0615.05002 [11] Stanley, R., Enumerative combinatorics volume 2, Cambridge studies in advanced mathematics 62, (1999), Cambridge University Press UK [12] Stankova, Z.E., Forbidden subsequences, Discrete math., 132, 291-316, (1994) · Zbl 0810.05011 [13] Stankova, Z.E., Classification of forbidden subsequences of length 4, Europ. J. combinatorics, 17, 501-517, (1996) · Zbl 0857.05007 [14] Tarjan, R.E., Sorting using networks of queues and stacks, J. ACM, 19, 341-346, (1972) · Zbl 0243.68004 [15] West, J., Generating trees and the Catalan and Schröder numbers, Discrete math., 146, 247-262, (1995) · Zbl 0841.05002
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