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On symmetries and parallelogram spaces.

Mirko Polonijo (1985)

Stochastica

The notion of a TST-space is introduced and its connection with a parallelogram space is given. The existence of a TST-space is equivalent to the existence of a parallelogram space, which is a new characterization of a parallelogram space. The structure of a TST-space is described in terms of an abelian group.

On the f - and h -triangle of the barycentric subdivision of a simplicial complex

Sarfraz Ahmad (2013)

Czechoslovak Mathematical Journal

For a simplicial complex Δ we study the behavior of its f - and h -triangle under the action of barycentric subdivision. In particular we describe the f - and h -triangle of its barycentric subdivision sd ( Δ ) . The same has been done for f - and h -vector of sd ( Δ ) by F. Brenti, V. Welker (2008). As a consequence we show that if the entries of the h -triangle of Δ are nonnegative, then the entries of the h -triangle of sd ( Δ ) are also nonnegative. We conclude with a few properties of the h -triangle of sd ( Δ ) .

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