Related papers: The generating function of two-stack sortable perm…

This paper has been withdrawn by the authors due to a major rewriting.

Motivated by the local flavor of several well-known semi-orthogonal decompositions in algebraic geometry, we introduce a technique called conservative descent, which shows that it is enough to establish these decompositions locally. The…

The (classical) problem of characterizing and enumerating permutations that can be sorted using two stacks connected in series is still largely open. In the present paper we address a related problem, in which we impose restrictions both on…

In this paper, algorithms are developed for computing the Stirling transform and the inverse Stirling transform; specifically, we investigate a class of sequences satisfying a two-term recurrence. We derive a general identity which…

Starting from some considerations we make about the relations between certain difference statistics and the classical permutation statistics we study permutations whose inversion number and excedance difference coincide. It turns out that…

This paper has been withdrawn by the author.

Recursive maps of high order of convergence $m$ (say $m=2^{10}$ or $m=2^{20}$) induce certain monotone step functions from which one can filter relevant information needed to globally separate and compute the real roots of a function on a…

This paper has been withdrawn due to a crucial error in the proof of the main theorem

In this, the eighth article in my Derived Langlands series, I describe the construction of a 2-variable L-function for two representations of general linear groups of a $p$-adic local field. Due to extenuating health circumstances, many of…

The generating polynomial of permutations of size $n$, counted by the number of alternating runs, has a root at $-1$ of multiplicity $\lfloor (n-2)/2 \rfloor$ for all $n \ge 2$. This result can be derived by combining the David--Barton…

The paper is withdrawn. The proof has an error and it requires a different approach.

A polynomial is real-rooted if all of its roots are real. For every polynomial $f(t) \in {\mathbf R}[t]$, the Hermite-Sylvester theorem associates a quadratic form $\Phi_2$ such that $f(t)$ is real-rooted if and only if $\Phi_2$ is positive…

Sequences are often conveniently encoded in the form of a generating function depending on a formal variable. This note presents two observations that allow one to draw conclusions about the generated sequence from the generating function.…

This paper has been withdrawn by the authors, due to issues concerning the use of unpublished experimental data.

A modified version of this paper is under process and with a new title and abstract. Hence, this version of the article is completely withdrawn.

In this paper, we introduce a new method for computing generating functions with respect to the number of descents and left-to-right minima over the set of permutations which have no consecutive occurrences of a pattern that starts with 1.

In this brief essay a construction of the $2$-variable L-function of Langlands is sketched in terms of monomial resolutions of admissible representations of reductive locally $p$-adic Lie groups.

Recent studies introduced biased (degree-dependent) edge percolation as a model for failures in real-life systems. In this work, such process is applied to networks consisting of two types of nodes with edges running only between nodes of…

This article has been withdrawn due to a mistake which is explained in version 2.

We prove a descent result for affine/projective varieties defined over an algebraically closed field. The idea is to work with the reduced Groebner basis of the ideal where the variety vanishes and study it's behaviour under group action…