Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Classifying Abelian Groups Through Acyclic Matchings
View through CrossRef
Abstract
The inquiry into identifying sets of monomials that can be eliminated from a generic homogeneous polynomial via a linear change of coordinates was initiated by E. K. Wakeford. This linear algebra problem prompted C. K. Fan and J. Losonczy to introduce the notion of acyclic matchings in the additive group
$$\mathbb {Z}^n$$
Z
n
, subsequently extended to abelian groups by the latter author. Alon, Fan, Kleitman, and Losonczy established the acyclic matching property for
$$\mathbb {Z}^n$$
Z
n
. This note aims to classify all abelian groups with respect to the acyclic matching property.
Title: Classifying Abelian Groups Through Acyclic Matchings
Description:
Abstract
The inquiry into identifying sets of monomials that can be eliminated from a generic homogeneous polynomial via a linear change of coordinates was initiated by E.
K.
Wakeford.
This linear algebra problem prompted C.
K.
Fan and J.
Losonczy to introduce the notion of acyclic matchings in the additive group
$$\mathbb {Z}^n$$
Z
n
, subsequently extended to abelian groups by the latter author.
Alon, Fan, Kleitman, and Losonczy established the acyclic matching property for
$$\mathbb {Z}^n$$
Z
n
.
This note aims to classify all abelian groups with respect to the acyclic matching property.
Related Results
The Removal Lemma: algebraic versions and applications
The Removal Lemma: algebraic versions and applications
This thesis presents some contributions in additive combinatorics and arithmetic Ramsey theory. More specifically, it deals with the interaction between combinatorics, number theor...
Disjoint Compatibility Graph of Non-Crossing Matchings of Points in Convex Position
Disjoint Compatibility Graph of Non-Crossing Matchings of Points in Convex Position
Let $X_{2k}$ be a set of $2k$ labeled points in convex position in the plane. We consider geometric non-intersecting straight-line perfect matchings of $X_{2k}$. Two such matchings...
NJ-Abelian Rings: an Abelian-Like Approach
NJ-Abelian Rings: an Abelian-Like Approach
This article extends the concept of NJ-semicommutative rings to introduce the broader class of NJ-abelian rings, which are defined by properties involving nilpotent elements and th...
Chern-Simons-Antoniadis-Savvidy Forms and Non-Abelian Anomaly
Chern-Simons-Antoniadis-Savvidy Forms and Non-Abelian Anomaly
Kuat medan tensor yang ditransformasikan secara homogen terhadap perluasan transformasi gauge memenuhi bentuk sifat invarian gauge. Analisa invarian gauge dalam bantuk integeralnya...
Self-dual codes over $\mathbb{F}_{q}+u\mathbb{F}_{q}+u^2\mathbb{F}_{q}$ and applications
Self-dual codes over $\mathbb{F}_{q}+u\mathbb{F}_{q}+u^2\mathbb{F}_{q}$ and applications
Self-dual codes over finite fields and over some finite rings have been of interest and extensively studied due to their nice algebraic structures and wide applications. Recently, ...
Incidence matrices for matchings
Incidence matrices for matchings
Abstract
LetM(n) denote the set of all matchings of the complete graph Kn. Set t =[ ]. For 0 ≤ k < l ≤ t−k ≤ t, letM(k, l) denote the incidence matrix of the car...
Strategic manipulation of preferences in the rank minimization mechanism
Strategic manipulation of preferences in the rank minimization mechanism
AbstractWe consider one-sided matching problems, where agents are allocated items based on stated preferences. Posing this as an assignment problem, the average rank of obtained ma...