Partially Well-Ordered Closed Sets of Permutations
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
It is known that the “pattern containment” order on permutations is not a partial well-order. Nevertheless, many naturally defined subsets of permutations are partially well-ordered, in which case they have a strong finite basis property. Several classes are proved to be partially well-ordered under pattern containment. Conversely, a number of new antichains are exhibited that give some insight as to where the boundary between partially well-ordered and not partially well-ordered classes lies.
- Atkinson, M. D. (1999) Restricted permutations, Discrete Math. 195, 27–38.
- Atkinson, M. D. and Stitt, T. Restricted permutations and the wreath product, In preparation.
- Atkinson, M. D. (1998) Permutations which are the union of an increasing and a decreasing sequence, Electron. J. Combin. 5, Paper R6.
- Atkinson, M. D. (1998) Generalised stack permutations, Combinatorics, Probability and Computing 7, 239–246.
- Atkinson, M. D. and Beals, R. Finiteness conditions on closed classes of permutations, unpublished.
- Bose, P., Buss, J. F. and Lubiw, A. (1998) Pattern matching for permutations, Inform. Process. Lett. 65, 277–283.
- Cohen, D. I. A. (1978) Basic Techniques of Combinatorial Theory, Wiley, New York.
- Higman, G. (1952) Ordering by divisibility in abstract algebras, Proc. London Math. Soc. 2, 326–336.
- Knuth, D. E. (1967) Fundamental Algorithms, The Art of Computer Programming, Vol. 1, 1st edn, Addison-Wesley, Reading, Mass.
- Lakshmibai, V. and Sandhya, B. (1990) Criterion for smoothness of Schubert varieties, Proc. Indian Acad. Sci. Math. Sci. 100, 45–52.
- Murphy, M. M., Ph.D. Thesis, University of St Andrews, in preparation.
- Shapiro, L. and Stephens, A. B. (1991) Bootstrap percolation, the Schöder number, and the N-kings problem, SIAM J. Discrete Math. 2, 275–280.
- Pratt, V. R. (1973) Computing permutations with double-ended queues, parallel stacks and parallel queues, Proc. ACM Symp. Theory of Computing 5, 268–277.
- Simion, R. and Schmidt, F. W. (1985) Restricted permutations, European J. Combin. 6, 383–406.
- Spielman, D. A. and Bóna, M. (2000) An infinite antichain of permutations, Note N2, Electron. J. Combin. 7(1).
- Stankova, Z. E. (1994) Forbidden subsequences, Discrete Math. 132, 291–316.
- Stankova, Z. E. (1996) Classification of forbidden subsequences of length 4, European J. Combin. 17(5), 501–517.
- Tarjan, R. E. (1972) Sorting using networks of queues and stacks, J. ACM 19, 341–346.
- West, J. (1996) Generating trees and forbidden sequences, Discrete Math. 157, 363–374.
- Partially Well-Ordered Closed Sets of Permutations
Volume 19, Issue 2 , pp 101-113
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- finite basis
- partial well-order
- pattern containment
- Industry Sectors