منابع مشابه
R. McNeill Alexander
What does it mean for a molecule to generate force? A good way to think about the force generated by a molecular machine is that force is one of the products of the cyclic, fuelconsuming chemical reaction. If the chemical reaction is favorable it will go forward even against a moderate load force. But if the force is too high, then it will inhibit the reaction, just like a high concentration of...
متن کاملNested Set Complexes for Posets and the Bier Construction
We generalize the concept of combinatorial nested set complexes to posets and exhibit the topological relationship between the arising nested set complexes and the order complex of the underlying poset. In particular, a sufficient condition is given so that this relationship is actually a subdivision. We use the results to generalize the proof method of Čukić and Delucchi, so far restricted to ...
متن کاملA PROBLEM ON INDEPENDENT r-TUPLES
then G(n ; l) contains k independent edges . It is easy to see that the above result is best possible since the complete graph of 2k-1 vertices and the graph of vertices x1, . . ., xk-1 ; Yl, • • •, Yn-k+l and edges (x1 , xj), 1I ; (x1 , y), 1 i :!-< k 1, 1-yj :!5 n k + 1 clearly does not contain k independent edges . By an r-graph o(r) we shall mean a graph whose basic elements are its vertice...
متن کاملIndependence Complexes and Edge Covering Complexes via Alexander Duality
The combinatorial Alexander dual of the independence complex Ind(G) and that of the edge covering complex EC(G) are shown to have isomorphic homology groups for each non-null graph G. This yields isomorphisms of homology groups of Ind(G) and EC(G) with homology dimensions being appropriately shifted and restricted. The results exhibits the complementary nature of homology groups of Ind(G) and E...
متن کاملBier Spheres and Posets
In 1992 Thomas Bier presented a strikingly simple method to produce a huge number of simplicial (n− 2)-spheres on 2n vertices as deleted joins of a simplicial complex on n vertices with its combinatorial Alexander dual. Here we interpret his construction as giving the poset of all the intervals in a boolean algebra that “cut across an ideal.” Thus we arrive at a substantial generalization of Bi...
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ژورنال
عنوان ژورنال: Publications de l'Institut Mathematique
سال: 2018
ISSN: 0350-1302,1820-7405
DOI: 10.2298/pim1818001j