相关论文: The generating function of two-stack sortable perm…
In this paper a method of constructing a semiorthogonal decomposition of the derived category of $G$-equivariant sheaves on a variety $X$ is described, provided that the derived category of sheaves on $X$ admits a semiorthogonal…
In this paper, we find distribution of descents over $(n-3)$- and $(n-4)$-stack-sortable permutations in terms of Eulerian polynomials. Our results generalize the enumeration results by Claesson, Dukes, and Steingr\'{\i}msson on $(n-3)$-…
A permutation can be locally classified according to the four local types: peaks, valleys, double rises and double falls. The corresponding classification of binary increasing trees uses four different types of nodes. Flajolet demonstrated…
The paper is withdrawn.
This paper was withdrawn by arXiv administrators. It is an erroneous duplicate submission of math.NA/0405095.
We study a sorting machine consisting of two stacks in series where the first stack has the added restriction such that entries in the stack must be in decreasing order from top to bottom. We give the basis of the class of permutations that…
By using the matrix formulation of the two-step approach to distributions of patterns in random sequences, recurrence and explicit formulas for the generating functions of successions in random permutations of arbitrary multisets are…
We present (bi-)symmetric generating functions for the joint distributions of Euler-Stirling statistics on permutations, including the number of descents ($\mathsf{des}$), inverse descents ($\mathsf{ides}$), the number of left-to-right…
For an effective Cartier divisor D on a scheme X we may form an nth root stack. Its derived category is known to have a semiorthogonal decomposition with components given by D and X. We show that this decomposition is 2n-periodic. For n=2…
I also submitted this paper as math.GR/0112109... it is therefore withdrawn from math.GR/0104076
In this paper we compute the bivariate generating function of $\gamma$-matchings over two backbones, filtered by the number of arcs and the topological genus. $\gamma$-matchings over two backbones are chord-diagrams, obtained via…
This paper has been withdrawn by the corresponding author because the newest version is now published in Journal of Discrete Algorithms.
This paper has been withdrawn by the author.The formula which was proposed gives only a second order deformation.
Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…
This paper has been withdrawn by the author as it has been divided into two separate papers.
This paper has been withdrawn by the authors due to its publication
This paper has been withdrawn by the author because Conjecture 1 is false. Please see arXiv:0901.2093 for a justification that Conjecture 1 is false. The other main results are also available from the above URL.
This paper is being withdrawn because another paper by the author makes it obsolete. See comments for directions to new paper.
At the end of the 1960s, Knuth characterised the permutations that can be sorted using a stack in terms of forbidden patterns. He also showed that they are in bijection with Dyck paths and thus counted by the Catalan numbers. Subsequently,…
Permutation rational functions over finite fields have attracted high interest in recent years. However, only a few of them have been exhibited. This article studies a class of permutation rational functions constructed using trace maps on…