相关论文: The generating function of two-stack sortable perm…
Let $G$ be a real-reductive Lie group and let $G_1$ and $G_2$ be two subgroups given by involutions. We show how the technique of gradient maps can be used in order to obtain a new proof of Matsuki's parametrization of the closed double…
This paper has been withdrawn by the author to comply with the journal policy to which it has been submitted.
Withdrawn paper because the results are recycled in several other papers and a new definition of T-homotopy is proposed in math.AT/0505152.
This paper has been withdrawn by the author because of copyright reasons.
This work is a continuation of some recent articles presenting enumerative results for Catalan words avoiding one or a pair of consecutive or classical patterns of length $3$. More precisely, we provide systematically the bivariate…
This paper has been withdrawn by the author because of finding a flaw in the proof of endogeny for the Frozen Percolation RDE which was one of two examples discussed in this paper. The other example is correct and can be obtained from the…
Machines whose main purpose is to permute and sort data are studied. The sets of permutations that can arise are analysed by means of finite automata and avoided pattern techniques. Conditions are given for these sets being enumerated by…
This paper has been withdrawn because the analytic estimates are not confirmed by the numerical calculation of Nilles, Peloso and Sorbo (hep-ph/0102264 and hep-th/0103202).
The aim of this paper is by using generating functions to further study some identities and properties on the degenerate Stirling numbers of the second kind, the degenerate $r$-Stirling numbers of the second kind, the degenerate Stirling…
We introduce a lifting of West's stack-sorting map $s$ to partition diagrams, which are combinatorial objects indexing bases of partition algebras. Our lifting $\mathscr{S}$ of $s$ is such that $\mathscr{S}$ behaves in the same way as $s$…
This paper has been withdrawn.
Centrosymmetric involutions in the symmetric group S_{2n} are permutations \pi such that \pi=\pi^{-1} and \pi(i)+\pi(2n+1-i)=2n+1 for all i, and they are in bijection with involutions of the hyperoctahedral group. We describe the…
Beta Rank Function (BRF) is a two-sided distribution characterized by a smooth peak and double powerlaw decay, widely used to model empirical data exhibiting deviations from pure power laws. In this paper, we introduce a novel two-step…
Stacks have become a prevalent tool in studying problems with connections to String Theory, hence we see a need to develop a theory of supersymmetric stacks proper. We first define derived stacks on $\mathbb{Z}_2$-bi-graded k-modules…
We extend and generalize many of the enumerative results concerning West's stack-sorting map $s$. First, we prove a useful theorem that allows one to efficiently compute $|s^{-1}(\pi)|$ for any permutation $\pi$, answering a question of…
Noticing that some recent variations of descent polynomials are special cases of Carlitz and Scoville's four-variable polynomials, which enumerate permutations by the parity of descent and ascent positions, we prove a $q$-analogue of…
This is the first in a series of papers on rank decompositions of the matrix multiplication tensor. In this paper we: establish general facts about rank decompositions of tensors, describe potential ways to search for new matrix…
Let $s$ denote West's stack-sorting map. A permutation is called $t-\textit{sorted}$ if it is of the form $s^t(\mu)$ for some permutation $\mu$. We prove that the maximum number of descents that a $t$-sorted permutation of length $n$ can…
We study commutative ring structures on the integral span of rooted trees and $n$-dimensional skew shapes. The multiplication in these rings arises from the smash product operation on monoid representations in pointed sets. We interpret…
This submission has been withdrawn and replaced with the paper "Non-existence of torically maximal hypersurfaces" arXiv:1506.02813.