Enumeration of $4 \times 4$ magic squares

DOI10.1090/S0025-5718-10-02347-1zbMath1227.05092arXiv0907.3188OpenAlexW2907794874MaRDI QIDQ3081302

Andrew van Herick, Matthias Beck

Publication date: 7 March 2011

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0907.3188

zbMATH Keywords

arrangement of hyperplanesEhrhart theorymagic squarelattice-point countingrational inside-out convex polytoperational generating function computation

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Combinatorics in computer science (68R05) Orthogonal arrays, Latin squares, Room squares (05B15) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Graph labelling (graceful graphs, bandwidth, etc.) (05C78)

Related Items (1)

A fast algorithm for computing the number of magic series

Uses Software

• cdd
• PARI/GP
• barvinok
• PolyLib
• IOP

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An enumerative geometry for magic and magilatin labellings
• Constructing all magic squares of order three
• Computing the Ehrhart polynomial of a convex lattice polytope
• Inside-out polytopes
• Linear homogeneous Diophantine equations and magic labelings of graphs
• Computing the Continuous Discretely
• Six Little Squares and How Their Numbers Grow
• The Number of "Magic" Squares, Cubes, and Hypercubes

This page was built for publication: Enumeration of $4 \times 4$ magic squares