# Magic labelings of graphs, symmetric magic squares, systems of parameters, and Cohen-Macaulay rings

@article{Stanley1976MagicLO, title={Magic labelings of graphs, symmetric magic squares, systems of parameters, and Cohen-Macaulay rings}, author={Richard P. Stanley}, journal={Duke Mathematical Journal}, year={1976}, volume={43}, pages={511-531} }

## 69 Citations

Magic graphs and the faces of the Birkhoff polytope

- Mathematics
- 2004

Author(s): Ahmed, Maya Mohsin | Abstract: Magic labelings of graphs are studied in great detail by Stanley and Stewart. In this article, we construct and enumerate magic labelings of graphs using…

Ehrhart polynomials, simplicial polytopes, magic squares and a conjecture of Stanley

- Mathematics
- 2003

Abstract It is proved that for a certain class of integer polytopes P the polynomial h(t ) which appears as the numerator in the Ehrhart series of P, when written as a rational function of t, is…

On multi-symmetric functions and transportation polytopes

- MathematicsProyecciones (Antofagasta)
- 2022

We present a study of the transportation polytopes appearing in the product rule of elementary multi-symmetric functions introduced by F. Vaccarino.

Realization of digraphs in Abelian groups and its consequences

- MathematicsJ. Graph Theory
- 2022

Let G→ be a directed graph of order n with no component of order less than 3, and let Γ be a finite Abelian group such that ∣Γ∣≥2n+2n or if n is large enough with respect to an arbitrarily fixed ε>0…

Enumerating Magic Distinct Labellings of the Cube

- Mathematics
- 2021

We find by applying MacMahon’s partition analysis that all magic labellings of the cube are of eight types, each generated by six basis elements. A combinatorial proof of this fact is given. The…

The integer-magic spectra and null sets of the Cartesian product of trees

- MathematicsAustralas. J Comb.
- 2018

A PROJECT SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY Michael Aidan McKeown IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE

- Mathematics
- 2017

A vertex-magic group edge labeling of a graph G(V,E) with |E| = n is an injection from E to an abelian group Γ of order n such that the sum of labels of all incident edges of every vertex x ∈ V is…

## References

SHOWING 1-10 OF 21 REFERENCES

GRAPHS SYSTEMS OF PARAMETERS

- GRAPHS SYSTEMS OF PARAMETERS
- 1974

Toroidal Embeddings I, Lecture Notes in Math

- Toroidal Embeddings I, Lecture Notes in Math
- 1973

Rings of Invariants of Tori, Cohen-Macaulay Rings Generated by Monomials, and Polytopes

- Mathematics
- 1972

Cohen-Macaulay rings, invariant theory, and the generic perfection q[ determinantal loci

- American J. Mth
- 1971

Invariant theory and the generic perfection of determinantal loci

- Mathematics
- 1971

0. Introduction. Let R be a commutative Noetherian ring with identity and let I be a proper ideal of R. A classical result of Krull is that if I can be generated by r elements then the rank or…

Introduction to commutative algebra

- Mathematics
- 1969

* Introduction * Rings and Ideals * Modules * Rings and Modules of Fractions * Primary Decomposition * Integral Dependence and Valuations * Chain Conditions * Noetherian Rings * Artin Rings *…