The cyclic coloring complex of a complete k-uniform hypergraph

In this paper, we study the homology of the cyclic coloring complex of three different types of $k$-uniform hypergraphs. For the case of a complete $k$-uniform hypergraph, we show that the dimension of the $(n-k-1)^{st}$ homology group is given by a binomial coefficient. Further, we discuss a complex whose $r$-faces consist of all ordered set partitions $[B_1, ..., B_{r+2}]$ where none of the $B_i$ contain a hyperedge of the complete $k$-uniform hypergraph $H$ and where $1 \in B_1$. It is shown that the dimensions of the homology groups of this complex are given by binomial coefficients. As a consequence, this result gives the dimensions of the multilinear parts of the cyclic homology groups of \C[x_1,...,x_n]/ \{x_{i_1}...x_{i_k} \mid i_{1}...i_{k} is a hyperedge of $H \}$. For the other two types of hypergraphs, star hypergraphs and diagonal hypergraphs, we show that the dimensions of the homology groups of their cyclic coloring complexes are given by binomial coefficients as well

EFFECT ON MILK PRODUCTION AND INCOME OVER FEED COST FROM FOLLOWING LESS THAN OPTIMUM MANAGEMENT STRATEGIES RELATED TO DAIRY COW REPLACEMENT

Livestock Production/Industries,

Hyperoctahedral Eulerian Idempotents, Hodge Decompositions, and Signed Graph Coloring Complexes

Phil Hanlon proved that the coefficients of the chromatic polynomial of a graph G are equal (up to sign) to the dimensions of the summands in a Hodge-type decomposition of the top homology of the coloring complex for G. We prove a type B analogue of this result for chromatic polynomials of signed graphs using hyperoctahedral Eulerian idempotents

Asymmetric 22-colorings of graphs

We show that the edges of every 3-connected planar graph except $K_4$ can be colored with two colors in such a way that the graph has no color preserving automorphisms. Also, we characterize all graphs which have the property that their edges can be $2$-colored so that no matter how the graph is embedded in any orientable surface, there is no homeomorphism of the surface which induces a non-trivial color preserving automorphism of the graph

Violence, Cruelty, Power: Reflections on Heteronomy

There is an opening in Castoriadis' work for a notion of cruelty, and it emerges in the way in which he develops his idea of heteronomy, as a human world that is blinded or deflected away from human self-creation. This essay is an attempt to locate cruelty constitutively or ontologically in a post-metaphysical register, as an act of creativity that can be given form as a very particular act of singularity, that is, without regard for the other. Acts of human cruelty are acts of imaginary, creative activity among others that themselves are form, that is, expressed in physically embodied, objectivated, linguistic or symbolic form, and often become highly stylized, and when socially instituted, have their own spatial and temporal dimensions. In this way, it is distinct from relations of power