相关论文: The generating function of two-stack sortable perm…
By means of the generating function method, a linear recurrence relation is explicitly resolved. The solution is expressed in terms of the Stirling numbers of both the first and the second kind. Two remarkable pairs of combinatorial…
The circular descent of a permutation $\sigma$ is a set $\{\sigma(i)\mid \sigma(i)>\sigma(i+1)\}$. In this paper, we focus on the enumerations of permutations by the circular descent set. Let $cdes_n(S)$ be the number of permutations of…
This paper has been withdrawn by the author due to a sheaf-theoretic error, in the end of the proof of the main theorem.
In this note we consider the question how the set of inversions of a permutation $\pi \in S_n$ can be partitioned into two subset, such that those are itself inversion sets of permutations. This is archived by exploiting a connection to a…
A ballot permutation is a permutation {\pi} such that in any prefix of {\pi} the descent number is not more than the ascent number. In this article, we obtained a formula in close form for the multivariate generating function of {A(n,d,j)},…
A general explicit form for generating functions for approximating fractional derivatives is derived. To achieve this, an equivalent characterisation for consistency and order of approximations established on a general generating function…
The descent set D(w) of a permutation w of 1,2,...,n is a standard and well-studied statistic. We introduce a new statistic, the connectivity set C(w), and show that it is a kind of dual object to D(w). The duality is stated in terms of the…
A finite irreducible real reflection group of rank l and Coxeter number h has root system of cardinality h*l. It is shown that the fake degree for the permutation action on its roots is divisible by [h]_q = 1+q+q^2+...+q^{h-1}, and that in…
In this paper we give an ordinal analysis of the theory of second order arithmetic. We do this by working with proof trees -- that is, "deductions" which may not be well-founded. Working in a suitable theory, we are able to represent…
In the 60's, Knuth introduced stack-sorting and serial compositions of stacks. In particular, one significant question arise out of the work of Knuth: how to decide efficiently if a given permutation is sortable with 2 stacks in series?…
This paper has been withdrawn by the author, due to errors in Groebner basis calculations in the cases of five and six dimensional groups.
We give two determinantal representations for a bivariate polynomial. They may be used to compute the zeros of a system of two of these polynomials via the eigenvalues of a two-parameter eigenvalue problem. The first determinantal…
We give a characteristic free proof of the main result of our previous paper (math.AC/0509697) concerning toroidalization of generating sequences of valuations in dimension two function fields. We show that when an extension of two…
We prove that the genus polynomials of the graphs called iterated claws are real-rooted. This continues our work directed toward the 25-year-old conjecture that the genus distribution of every graph is log-concave. We have previously…
The paper is being withdrawn. A new submission will follow.
This paper has been administratively withdrawn by arXiv, duplicate of arXiv:1008.2691.
This paper has been withdrawn by the author. Improved versions (arXiv:1109.5548 and arXiv:0708.4190) are accepted.
This paper has been withdrawn by the author, due to possible counter-examples.
This paper has been withdrawn by the author(s), due an error in the proof.
The paper has been withdrawn by authors. The issues studied in this paper were changed so much that we have published a new paper considering these issues. See hep-th/0406074