Consider a graph with rotation system, namely, for every vertex, circular ordering of the incident edges. Given such graph, an angle cover maps vertex to pair consecutive edges in -- that each edge participates at least one pair. We show any maximum degree 4 admits cover, give poly-time algorithm deciding if no degree-3 vertices has angle-cover, and prove that, given 5, it is NP-hard decide whe...

We show that the theta representations on certain covers of general linear groups support certain types of unique functionals. The proof involves two types of Fourier coefficients. The first are semi-Whittaker coefficients, which generalize coefficients introduced by Bump and Ginzburg for the double cover. The covers for which these coefficients vanish identically (resp. do not vanish for some ...

The biclique cover number (resp. biclique partition number) of a graph G, bc(G) (resp. bp(G)), is the least number of bicliques—complete bipartite subgraphs—that are needed to cover (resp. partition) the edges of G. The local biclique cover number (resp. local biclique partition number) of a graph G, lbc(G) (resp. lbp(G)), is the least r such that there is a cover (resp. partition) of the edges...