相关论文: On short expressions for cosets of permutation sub…
Helfgott and Seress have proved the existence of a quasipolynomial upper bound on the diameter of $\mathrm{Alt}(n)$. In this paper, we walk partway towards removing the dependence on CFSG from that result, by using the algorithm solving the…
The minimal degree of a permutation group $G$ is the minimum number of points not fixed by non-identity elements of $G$. Lower bounds on the minimal degree have strong structural consequences on $G$. Babai conjectured that if a primitive…
This thesis provides an explanation of L\'aszl\'o Babai's quasi-polynomial algorithm for the Graph Isomorphism Problem published in 2015 with a particular focus on the case of local certificates, i.e. the case that cannot be dealt with by…
Stanley's formula for the number of reduced expressions of a permutation regarded as a Coxeter group element raises the question of how to enumerate the reduced expressions of an arbitrary Coxeter group element. We provide a framework for…
We obtain a weaker but still quasipolynomial version of Babai's famous GI-algorithm.
We extend Babai's quasipolynomial-time graph isomorphism test (STOC 2016) and develop a quasipolynomial-time algorithm for the multiple-coset isomorphism problem. The algorithm for the multiple-coset isomorphism problem allows to exploit…
We consider the problem of factoring permutations as a product of special types of transpositions, namely, those transpositions involving two positions with bounded distances. In particular, we investigate the minimum number, $\delta$, such…
Motivated by issues arising in computer science, we investigate the loop-free paths from the identity transformation and corresponding straight words in the Cayley graph of a finite transformation semigroup with a fixed generator set. Of…
We explore various techniques to compress a permutation $\pi$ over n integers, taking advantage of ordered subsequences in $\pi$, while supporting its application $\pi$(i) and the application of its inverse $\pi^{-1}(i)$ in small time. Our…
A characterization of finitely generated shift-invariant subspaces is given when generators are g-minimal. An algorithm is given for the determination of the coefficients in the well known representation of the Fourier transform of an…
This note presents an elementary version of Sims's algorithm for computing strong generators of a given perm group, together with a proof of correctness and some notes about appropriate low-level data structures. Upper and lower bounds on…
Coherent configurations (CCs) are highly regular colorings of the set of ordered pairs of a "vertex set"; each color represents a "constituent digraph." CCs arise in the study of permutation groups, combinatorial structures such as…
Any permutation in the finite symmetric group can be written as a product of simple transpositions $s_i = (i~i+1)$. For a fixed permutation $\sigma \in \mathfrak{S}_n$ the products of minimal length are called reduced decompositions or…
Computational asymmetry, i.e., the discrepancy between the complexity of transformations and the complexity of their inverses, is at the core of one-way transformations. We introduce a computational asymmetry function that measures the…
A permutation $\pi: [n] \rightarrow [n]$ is a Baxter permutation if and only if it does not contain either of the patterns $2-41-3$ and $3-14-2$. Baxter permutations are one of the most widely studied subclasses of general permutation due…
A wide range of applications, most notably in comparative genomics, involve the computation of a shortest sorting sequence of operations for a given permutation, where the set of allowed operations is fixed beforehand. Such sequences are…
The isomorphism problem for finite groups of order n (GpI) has long been known to be solvable in $n^{\log n+O(1)}$ time, but only recently were polynomial-time algorithms designed for several interesting group classes. Inspired by recent…
We determine a condition on the minimum Hamming weight of some special abelian group codes and, as a consequence of this result, we establish that any such code is, up to permutational equivalence, a subspace of the direct sum of $s$ copies…
The group isomorphism problem in computational complexity asks whether two finite groups given by their Cayley tables are isomorphic or not. Although polynomial-time isomorphism tests exist for many specific types of groups, no general…
In the first section of this senior thesis the author provides some new efficient algorithms for calculating with finite permutation groups. They cannot be found in the computer algebra system MAGMA, but they can be implemented there. For…