14 citations · 48 across the 28 of their papers we have counts for
6 papers · 1 filter
On the Enumeration of Interval Graphs
Joyce C. Yang, Nicholas Pippenger
We present upper and lower bounds for the number of interval graphs on vertices. Answering a question posed by Hanlon, we show that the ordinary generating function $I(x)…
A Combinatorial Interpretation of the Joint Cumulant
Connor Ahlbach, Jeremy Usatine, Nicholas Pippenger
In this paper, we apply the combinatorial proof technique of Description, Involution, Exceptions (DIE) to prove various known identities for the joint cumulant. Consider a set of r…
Barred Preferential Arrangements
Connor Ahlbach, Jeremy Usatine, Nicholas Pippenger
A preferential arrangement of a set is a total ordering of the elements of that set with ties allowed. A barred preferential arrangement is one in which the tied blocks of elements…
A Census of Vertices by Generations in Regular Tessellations of the Plane
Alice Paul, Nicholas Pippenger
We consider regular tessellations of the plane as infinite graphs in which edges and faces meet at each vertex, and in which edges and vertices surround each face.…
The Hypercube of Resistors, Asymptotic Expansions, and Preferential Arrangements
Nicholas Pippenger
Motivated by the problem of finding resistances among vertices in a hypercube, we derive exact expressions, generating functions, and asymptotic expansions for these resistances, t…
Random cyclations
Nicholas Pippenger
Consider n unit intervals, say [1,2], [3,4], ..., [2n-1,2n]. Identify their endpoints in pairs at random, with all (2n-1)!! = (2n-1) (2n-3) ... 3 1 pairings being equally likely. T…