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Lattice Polynomials, 12312-Avoiding Partial Matchings and Even Trees
Lattice Polynomials Partial Matchings Even Trees
2010/11/22
The lattice polynomials $L_{i,j}(x)$ are introduced by Hough and Shapiro as a weighted count of certain lattice paths from the origin to the point $(i,j)$. In particular, $L_{2n, n}(x)$ reduces to th...
A new subgroup lattice characterization of finite solvable groups
subgroup lattice characterization solvable groups
2010/11/18
We show that if G is a finite group then no chain of modular elements in its subgroup lattice L(G) is longer than a chief series. Also, we show that if G is a nonsolvable finite group then every maxi...
Lattice parameters from direct-space images at two tilts
Lattice parameters direct-space images
2010/11/2
Lattices in three dimensions are oft studied from the ``reciprocal space'' perspective of diffraction. Today, the full lattice of a crystal can often be inferred from direct-space information about t...