algebra   5480

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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 
yesterday 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 
yesterday 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 
7 days ago by geetarista

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