Related papers: Variations on the Post Correspondence Problem for …
Inspired by a planar partitioning problem involving multiple improper chambers, this article investigates using classical techniques what can be said of the existence, uniqueness, and regularity of minimizers in a certain free-endpoint…
The paper considers the problem of finding the number of dominant voters in two-level voting procedures. At the first stage, voting is conducted among local groups of voters, and at the second stage, the results are aggregated to form a…
While efficient algorithms are known for solving many important problems related to groups, no efficient algorithm is known for determining whether two arbitrary groups are isomorphic. The particular case of 2-nilpotent groups, a special…
Let $\mathscr{C}$ be a classical group defined over a finite field. We present comprehensive theoretical solutions to the following closely related problems: 1) List a representative for each conjugacy class of $\mathscr{C}$. 2) Given $x…
Multi-view learning is frequently used in data science. The pairwise correlation maximization is a classical approach for exploring the consensus of multiple views. Since the pairwise correlation is inherent for two views, the extensions to…
An exact, number-conserving solution to the generalized, orbit-dependent pairing problem is derived by introducing an infinite-dimensional algebra. A method for obtaining eigenvalues and eigenvectors of the corresponding Hamiltonian is also…
We compute the trace of an endomorphism in equivariant bivariant K-theory for a compact group G in several ways: geometrically using geometric correspondences, algebraically using localisation, and as a Hattori-Stallings trace. This results…
It is known that the number of homomorphisms from a group $F$ to a group $G$ is divisible by the greatest common divisor of the order of $G$ and the exponent of $F/[F,F]$. We investigate the number of homomorphisms satisfying some natural…
We raise the problem of constructing quantum observables that have classical counterparts without quantization. Specifically we seek to define and motivate a solution to the quantum-classical correspondence problem independent from…
We solve the word problem for free double categories without equations between generators by translating it to the word problem for 2-categories. This yields a quadratic algorithm deciding the equality of diagrams in a free double category.…
The Regular Post Embedding Problem extended with partial (co)directness is shown decidable. This extends to universal and/or counting versions. It is also shown that combining directness and codirectness in Post Embedding problems leads to…
We show that the moduli spaces of irreducible labeled parametrized marked rational curves in toric varieties can be embedded into algebraic tori such that their tropicalizations are the analogous tropical moduli spaces. These embeddings are…
We investigate the computational complexity of the problem of deciding if an algebra homomorphism can be factored through an intermediate algebra. Specifically, we fix an algebraic language, L, and take as input an algebra homomorphism f…
Starting from a generalization of the standard axioms for a monoid we present a stepwise development of various, mutually equivalent foundational axiom systems for category theory. Our axiom sets have been formalized in the Isabelle/HOL…
In this paper, we explore cooperative and competitive coupled obstacle systems, which, up to now, are new type obstacle systems and formed by coupling two equations belonging to classical obstacle problem. On one hand, applying the…
We determine all the multiplicity-free representations of the symmetric group. This project is motivated by a combinatorial problem involving systems of set-partitions with a specific pattern of intersection.
We address the problem of computing distances between rankings that take into account similarities between candidates. The need for evaluating such distances is governed by applications as diverse as rank aggregation, bioinformatics, social…
The computation of the normaliser of a permutation group in the full symmetric group is an important and hard problem in computational group theory. This article reports on an algorithm that builds a descending chain of overgroups to…
We give formulae for a module presentation of the module of identities among relations for a presentation of a group, in terms of information on 0- and 1-combings of the Cayley graph. This is seen as a special case of extending a partial…
It was noticed by Harel in [Har86] that "one can define $\Sigma_1^1$-complete versions of the well-known Post Correspondence Problem". We first give a complete proof of this result, showing that the infinite Post Correspondence Problem in a…