Jim Propp’s P-machine, also known as the ‘rotor router model’ is a simple deterministic process that simulates a random walk on a graph. Instead of distributing chips to ran...
Joshua N. Cooper, Benjamin Doerr, Joel H. Spencer,...
Given a graph we show how to construct a family of manifolds whose Euler characteristics are the values of the chromatic polynomial of the graph at various integers. The manifolds...
Let Φ be an irreducible root system and ∆ be a base for Φ; it is well known that any root in Φ is an integral combination of the roots in ∆. In comparison to this fact, we ...
A 3-connected matroid M is sequential or has path width 3 if its ground set E(M) has a sequential ordering, that is, an ordering (e1, e2, . . . , en) such that ({e1, e2, . . . , ek...
A minimal k-cycle is a family of sets A0, . . . , Ak−1 for which Ai ∩ Aj = ∅ if and only if i = j or i and j are consecutive modulo k. Let fr(n, k) be the maximum size of a ...
We sharpen a result of Hansel on separating set systems. We also extend a theorem of Spencer on completely separating systems by proving an analogue of Hansel’s result.
We present various techniques to count proportions of permutations with restricted cycle structure in finite permutation groups. For example, we show how a generalized block theo...
In a paper of Klazar, several counting examples for rooted plane trees were given, including matchings and maximal matchings. Apart from asymptotical analysis, it was shown how to...