arXiv subjects
Publications and source records attributed to Manuela Muzika Dizdarević.
Taylor varieties $\mathcal{T}^n_{d,e,m}$ arise from Taylor expansion of rational functions in $n$ variables. Among them, we look for non-defective hypersurfaces. We prove that the cases $n=2$ and $m=d+2$ give new examples of hypersurfaces with identically null Hessian.
Conway and Lagarias observed that a triangular region T(m) in a hexagonal lattice admits signed tiling by three-in-line polyominoes (tribones) if and only if m=9d-1 or m=9d for some integer d. We apply the theory of Groebner bases over integers to show that T(m) admits a signed tiling by n-in-line polyominoes (n-bones) if and only if m=dn^2-1 or m=dn^2 for some integer d. Explicit description of the Groebner basis allows us to calculate the "Groebner 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 of the $n$-in-line polyomino.