相关论文: Symmetry groups for social preference functions
In the theory of social choice the research is focused around the projection of individual preference orders to the social preference order. Also, the justification of the preference order formalism begins with the concept of utility i.e.…
When studying safety properties of (formal) protocol models, it is customary to view the scheduler as an adversary: an entity trying to falsify the safety property. We show that in the context of security protocols, and in particular of…
In this paper we study the parameterized complexity of two well-known permutation group problems which are NP-complete. 1. Given a permutation group G=<S>, subgroup of $S_n$, and a parameter $k$, find a permutation $\pi$ in G such that…
Tackling the problem of ordinal preference revelation and reasoning, we propose a novel methodology for generating an ordinal utility function from a set of qualitative preference statements. To the best of our knowledge, our proposal…
A common assumption in modern microeconomic theory is that choice should be rationalizable via a binary preference relation, which \citeauthor{Sen71a} showed to be equivalent to two consistency conditions, namely $\alpha$ (contraction) and…
The aim of the present survey paper is to provide an accessible introduction to a new chapter of representation theory - harmonic analysis for noncommutative groups with infinite-dimensional dual space. I omitted detailed proofs but tried…
An experimenter seeks to learn a subject's preference relation. The experimenter produces pairs of alternatives. For each pair, the subject is asked to choose. We argue that, in general, large but finite data do not give close…
A skew-morphism of a finite group $G$ is a permutation $\s$ on $G$ fixing the identity element, and for which there exists an integer function $\pi$ on $G$ such that $\s(xy)=\s(x)\s^{\pi(x)}(y)$ for all $x,y\in G$. It has been known that…
Neural representations are not unique objects. Even when two systems realize the same downstream computation, their hidden coordinates may differ by reparameterization. A probe family intended to reveal structure already present in a…
If a (possibly finite) compact Lie group acts effectively, locally linearly, and homologically trivially on a closed, simply-connected four-manifold with second Betti number at least three, then it must be isomorphic to a subgroup of S^1 x…
To solve two problems of Bergman stated in 1981, we construct a group $G$ such that $G$ contains a free noncyclic subgroup (hence, $G$ satisfies no group identity) and $G$, as a group, is generated by its subsemigroup that satisfies a…
We have found that known community identification algorithms produce inconsistent communities when the node ordering changes at input. We propose two metrics to quantify the level of consistency across multiple runs of an algorithm:…
The Ising model is the simplest to describe many-body effects in classical statistical mechanics. Duality analysis leads to a critical point under several assumptions. The Ising model itself has $Z(2)$ symmetry. The basis of the duality…
A combinatorial property of prositive group presentations, called completeness, is introduced, with an effective criterion for recognizing complete presentations, and an iterative method for completing an incomplete presentation. We show…
In this paper, we prove stability results about orthogonal groups over finite commutative rings where 2 is a unit. Inspired by Putman and Sam (2017), we construct a category $\mathbf{OrI}(R)$ and prove a Noetherianity theorem for the…
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
In recent years, the traditional notion of symmetry in quantum theory was expanded to so-called generalised or categorical symmetries, which, unlike ordinary group symmetries, may be non-invertible. This appears to be at odds with Wigner's…
Let K be a field of positive characteristic p, let R be either a group algebra K[G] or a restricted enveloping algebra u(L), and let I be the augmentation ideal of R. We first characterize those R for which I satisfies a polynomial identity…
Wigner's classification has led to the insight that projective unitary representations play a prominent role in quantum mechanics. The physics literature often states that the theory of projective unitary representations can be reduced to…
We introduce the notion of a weighted inversion statistic on the symmetric group, and examine its distribution on each conjugacy class. Our work generalizes the study of several common permutation statistics, including the number of…