algebra   5528

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[1603.00051] Algebraic Method in Tilings
In this paper we introduce a new algebraic method in tilings. Combining this method with Hilbert's Nullstellensatz we obtain a necessary condition for tiling n-space by translates of a cluster of cubes. Further, the polynomial method will enable us to show that if there exists a tiling of n-space by translates of a cluster V of prime size then there is a lattice tiling by V as well. Finally, we provide supporting evidence for a conjecture that each tiling by translates of a prime size cluster V is lattice if V generates n-space.
polyominoes  algebra  representation  rather-interesting  nudge-targets  consider:representation 
29 days ago by Vaguery
3Blue1Brown - YouTube - YouTube
good conceptual videos that really explain the fundamentals of various branches of math. The animations are excellent.
math  video  linear  algebra  calculus  topology  goodstuff 
29 days ago by brentfarwick
Course Notes -- J.S. Milne
Notes for graduate-level mathematics courses: Galois theory, groups, number theory, algebraic geometry, modular functions, abelian varieties, class field theory, etale cohomology.
math  algebra  liegroup  elliptic  geometry  grouptheory 
4 weeks ago by geetarista

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