14 citations · 48 across the 28 of their papers we have counts for
30 papers
A Formula for the Determinant
Nicholas Pippenger
We give a formula for the determinant of an matrix with entries from a commutative ring with unit. The formula can be evaluated by a "straight-line program" performing…
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)…
Self-intersections of Two-Dimensional Equilateral Random Walks and Polygons
Max B. Kutler, Margaret Rogers, Nicholas Pippenger
We study the mean and variance of the number of self-intersections of the equilateral isotropic random walk in the plane, as well as the corresponding quantities for isotropic equi…
Asymptotic Analysis of Run-Length Encoding
Nabil Zaman, Nicholas Pippenger
Gallager and Van Voorhis have found optimal prefix-free codes for a random variable that is geometrically distributed: for . We determine t…
Gap Theorems for the Delay of Circuits Simulating Finite Automata
Connor Ahlbach, Jeremy Usatine, Nicholas Pippenger
We study the delay (also known as depth) of circuits that simulate finite automata, showing that only certain growth rates (as a function of the number of steps simulated) are…
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…