14 citations · 48 across the 28 of their papers we have counts for
5 papers · 1 filter
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…
Elementary Proofs of the Main Limit Theorems of Probability
Nicholas Pippenger
We give simple proofs, under minimal hypotheses, of the Weak Law of Large Numbers and the Central Limit Theorem for independent identically distributed random variables. These proo…
Fault Tolerance in Cellular Automata at Low Fault Rates
Mark McCann, Nicholas Pippenger
A commonly used model for fault-tolerant computation is that of cellular automata. The essential difficulty of fault-tolerant computation is present in the special case of simply r…
Efficient Algorithms for Zeckendorf Arithmetic
Connor Ahlbach, Jeremy Usatine, Nicholas Pippenger
We study the problem of addition and subtraction using the Zeckendorf representation of integers. We show that both operations can be performed in linear time; in fact they can be…
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…