We give some new Wilf equivalences for signed patterns which allow the complete classification of signed patterns of lengths three and four. The problem is considered for pattern avoidance by general as well as involu...
详细信息
We give some new Wilf equivalences for signed patterns which allow the complete classification of signed patterns of lengths three and four. The problem is considered for pattern avoidance by general as well as involutive signed permutations. (C) 2007 Elsevier B.V. All rights reserved.
In 1985, Simion and Schmidt gave a constructive bijection phi from the set of all length (n - 1) binary strings having no two consecutive 1s to the set of all length n permutationsavoiding all patterns in {123,132,21...
详细信息
In 1985, Simion and Schmidt gave a constructive bijection phi from the set of all length (n - 1) binary strings having no two consecutive 1s to the set of all length n permutationsavoiding all patterns in {123,132,213}. In this paper, we generalize p to an injective function from {0,1}(n-1) to the set S. of all length n permutations and derive from it four bijections phi : P -> Q where P subset of{0,1}(n-1) and Q subset of S-n. The domains are sets of restricted binary strings and the codomains are sets of pattern-avoiding permutations. As a particular case we retrieve the original Simion-Schmidt bijection. We also show that the bijections obtained are actually combinatorial isomorphisms, i.e. closeness-preserving bijections. Three of them have known Gray codes and generating algorithms for their domains and we present similar results for each corresponding codomain, under the appropriate combinatorial isomorphism.
暂无评论