Related papers: Counting pop-stacked permutations in polynomial ti…
P(n,s) denotes the number of permutations of 1,2,...n that have exactly s sequences. Canfield and Wilf [math.CO/0609704] recently showed that P(n,s) can be written as a sum of s polynomials in n. We determine these polynomials explicitly…
We present a new algorithm for iterating over all permutations of a sequence. The algorithm leverages elementary~$O(1)$ operations on recursive lists. As a result, no new nodes are allocated during the computation. Instead, all elements are…
We propose investigating a summation analog of the paradigm for parallel integration. We make some first steps towards an indefinite summation method applicable to summands that rationally depend on the summation index and a P-recursive…
This paper is concerned with the complexity analysis of constructor term rewrite systems and its ramification in implicit computational complexity. We introduce a path order with multiset status, the polynomial path order POP*, that is…
A moldable job is a job that can be executed on an arbitrary number of processors, and whose processing time depends on the number of processors allotted to it. A moldable job is monotone if its work doesn't decrease for an increasing…
In this paper we study a class of dynamical systems generated by iterations of multivariate permutation polynomial systems which lead to polynomial growth of the degrees of these iterations. Using these estimates and the same techniques…
Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…
In many high-dimensional problems,polynomial-time algorithms fall short of achieving the statistical limits attainable without computational constraints. A powerful approach to probe the limits of polynomial-time algorithms is to study the…
We consider permutations sortable by $k$ passes through a deterministic pop stack. We show that for any $k\in\mathbb N$ the set is characterised by finitely many patterns, answering a question of Claesson and Gu{\dh}mundsson. Our…
The prime-counting function $\pi(x)$ which returns the number of primes smaller or equal to a given number is a topic of interest in number theory. An algorithm based on a cyclic group isomorphic to $Z/nZ$, the so-called $Z$-functions, was…
We consider a variant on the Tetranacci sequence, where one adds the previous four terms, then divides the sum by two until the result is odd. We give an algorithm for constructing "initially division-poor" sequences, where over an initial…
Permutations are usually enumerated by size, but new results can be found by enumerating them by inversions instead, in which case one must restrict one's attention to indecomposable permutations. In the style of the seminal paper by Simion…
The main purpose of this paper is to study the NP-complete subset-sum problem, not in the usual context of time-complexity-based classification of the algorithms (exponential/polynomial), but through a new kind of algorithmic classification…
We describe an algorithm, implemented in Python, which can enumerate any permutation class with polynomial enumeration from a structural description of the class. In particular, this allows us to find formulas for the number of permutations…
A polynomial-time algorithm is produced which, given generators for a group of permutations on a finite set, returns a direct product decomposition of the group into directly indecomposable subgroups. The process uses bilinear maps and…
We introduce an algorithm that conjectures the structure of a permutation class in the form of a disjoint cover of "rules"; similar to generalized grid classes. The cover is usually easily verified by a human and translated into an…
Imprecise probability is concerned with uncertainty about which probability distributions to use. It has applications in robust statistics and machine learning. We look at programming language models for imprecise probability. Our…
A polynomial-time algorithm for 0-1 integer linear programmings has been proposed. This method continues the classic idea of solving ILP with its LP relaxation. The innovation is that every constraint in the LP is reconstructed into a…
We study the behavior of West's stack-sorting map $s$ on permutations whose last entry is also their least. Let $S_{n}':=\{\pi0\mid \pi\in S_n\}$ where $\pi0$ denotes the concatenation of $\pi$ and $0$. For each permutation $\pi\in S_n'$,…
The paper investigates the problem of performing correlation analysis when the number of observations is very large. In such a case, it is often necessary to combine the random observations to achieve dimensionality reduction of the…