Tensor products of homotopy Gerstenhaber algebras

On the tensor product of two homotopy Gerstenhaber algebras we construct a Hirsch algebra structure which extends the canonical dg algebra structure. Our result applies more generally to tensor products of "level 3 Hirsch algebras" and also to the Mayer-Vietoris double complex.Comment: 13 pages; new Remark 5.4, minor change

Topological Prismatoids and Small Simplicial Spheres of Large Diameter

We introduce topological prismatoids, a combinatorial abstraction of the (geometric) prismatoids recently introduced by the second author to construct counter-examples to the Hirsch conjecture. We show that the `strong $d$-step Theorem' that allows to construct such large-diameter polytopes from `non-$d$-step' prismatoids still works at this combinatorial level. Then, using metaheuristic methods on the flip graph, we construct four combinatorially different non-$d$-step $4$-dimensional topological prismatoids with $14$ vertices. This implies the existence of $8$-dimensional spheres with $18$ vertices whose combinatorial diameter exceeds the Hirsch bound. These examples are smaller that the previously known examples by Mani and Walkup in 1980 ($24$ vertices, dimension $11$). Our non-Hirsch spheres are shellable but we do not know whether they are realizable as polytopes.Comment: 20 pages. Changes from v1 and v2: Reduced the part on shellability and general improvement to accesibilit

What does Hirsch index evolution explain us? A case study: Turkish Journal of Chemistry

The evolution of Turkish Journal of Chemistry (Turk J. Chem) Hirsch index (h-index) over the period 1995-2005 is studied and determined in the case of the self and without self-citations. It is seen that the effect of Hirsch index of Turk J. Chem has a highly positive trend during the last five years. It proves that Turk J. Chem is improving itself both in quantity and quality since h-index reflects peer review, and peer review reflects research quality of a journal.Comment: 5 pages, 3 figure