A pommaret division algorithm for computing Grobner bases in boolean rings

2008 ◽  
Author(s):  
Vladimir P. Gerdt ◽  
Mikhail V. Zinin
Keyword(s):  
Gröbner Bases ◽  
Grobner Bases ◽  
Division Algorithm ◽  
Boolean Rings

scholarly journals Signed polyomino tilings by n-in-line polyominoes and Gröbner bases

2016 ◽  
Vol 99 (113) ◽  
pp. 31-42 ◽  
Author(s):  
Manuela Muzika-Dizdarevic ◽  
Marinko Timotijevic ◽  
Rade Zivaljevic
Keyword(s):  
Homology Group ◽  
Hexagonal Lattice ◽  
Gröbner Bases ◽  
Grobner Bases ◽  
Explicit Description ◽  
Division Algorithm ◽  
Triangular Region ◽  
Newton Polynomial ◽  
Bner Bases ◽  
Bner Basis

Conway and Lagarias observed that a triangular region T(m) in a hexagonal lattice admits a signed tiling by three-in-line polyominoes (tribones) if and only if m 2 {9d?1, 9d}d2N. We apply the theory of Gr?bner bases over integers to show that T(m) admits a signed tiling by n-in-line polyominoes (n-bones) if and only if m 2 {dn2 ? 1, dn2}d2N. Explicit description of the Gr?bner basis allows us to calculate the ?Gr?bner discrete volume? of a lattice region by applying the division algorithm to its ?Newton polynomial?. Among immediate consequences is a description of the tile homology group for the n-in-line polyomino.

scholarly journals Gröbner bases for operads

2010 ◽  
Vol 153 (2) ◽  
pp. 363-396 ◽  
Author(s):  
Vladimir Dotsenko ◽  
Anton Khoroshkin
Keyword(s):  
Gröbner Bases ◽  
Grobner Bases

scholarly journals Gröbner bases over fields with valuations

2018 ◽  
Vol 88 (315) ◽  
pp. 467-483 ◽  
Author(s):  
Andrew J. Chan ◽  
Diane Maclagan
Keyword(s):  
Gröbner Bases ◽  
Grobner Bases
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