A note on enumerative counting

A Note on Counting Cuspidal

For geometrically nite Kleinian groups with parabolic elements we study that part of the Lagrange spectrum which does not lie in the Markov spectrum. Using the ergodicity of the associated geodesic ow with respect to the Liouville{Patterson measure, we obtain an estimate for the asymptotic frequency with which recurrent geodesics enter certain cusp regions. In particular, this allows a quantita...

A Note on Counting Isotropy Subgroups

Note on quantum counting classes∗

We define counting classes #BPP and #BQP as natural extensions of the classical well-studied one #P to the randomized and quantum cases. It is then shown that P#P = P#BQP.

Note on Counting Eulerian Circuits

We show that the problem of counting the number of Eulerian circuits in an undirected graph is complete for the class #P.

Note on the 3-graph counting lemma

Szemerédi’s regularity lemma proved to be a powerful tool in extremal graph theory. Many of its applications are based on the so-called counting lemma: if G is a kpartite graph with k-partition V1∪ · · ·∪Vk, |V1| = · · · = |Vk| = n, where all induced bipartite graphs G[Vi, Vj ] are (d, ε)-regular, then the number of k-cliques Kk in G is d( k 2)nk(1± o(1)). Frankl and Rödl extended Szemerédi’s r...