The classification of sets of permutations with forbidden subsequences of length 4 is not yet complete. (In my recent paper Classification offorbidden subsequences of length 4 submitted to European Journal of Combinatorics, Paris, this classification has been completed.) In this paper we show that I&(4132)( =(&(3142)/ by proving the stronger theorem for the corresponding permutation trees: T(4132)g T(3142). We give a new proof of the so-called Schriider result, some results on forbidding entire classes of symmetries of permutation matrices, and some conjectures concerning the basic question: for what permutations z and c it is true that I&(t)1 = IS,,(a)/ for all HEN. We also discuss possible attacks on cases similar to the Schriider result by ‘visualizing’ the structure of the corresponding permutations and generalize the method of permutation trees.
[1]
W. J. Thron,et al.
Encyclopedia of Mathematics and its Applications.
,
1982
.
[2]
L. Lovász.
Combinatorial problems and exercises
,
1979
.
[3]
Donald E. Knuth,et al.
PERMUTATIONS, MATRICES, AND GENERALIZED YOUNG TABLEAUX
,
1970
.
[4]
Julian West,et al.
Permutations with forbidden subsequences, and, stack-sortable permutations
,
1990
.
[5]
Doron Rotem,et al.
On a Correspondence Between Binary Trees and a Certain Type of Permutation
,
1975,
Inf. Process. Lett..
[6]
Daniel I. A. Cohen,et al.
Basic techniques of combinatorial theory
,
1978
.