24 citations · 32 across the 6 of their papers we have counts for
7 papers
Competition graphs induced by permutations
Brian Nakamura, Elizabeth Yang
In prior work, Cho and Kim studied competition graphs arising from doubly partial orders. In this article, we consider a related problem where competition graphs are instead induce…
On the Asymptotic Statistics of the Number of Occurrences of Multiple Permutation Patterns
Svante Janson, Brian Nakamura, Doron Zeilberger
We study statistical properties of the random variables , the number of occurrences of the pattern in the permutation . We present two contrasting approaches to this…
Using functional equations to enumerate 1324-avoiding permutations
Fredrik Johansson, Brian Nakamura
We consider the problem of enumerating permutations with exactly r occurrences of the pattern 1324 and derive functional equations for this general case as well as for the pattern…
Approaches for enumerating permutations with a prescribed number of occurrences of patterns
Brian Nakamura
In recent work, Zeilberger and the author used a functional equations approach for enumerating permutations with r occurrences of the pattern 12...k. In particular, the approach yi…
Using Noonan-Zeilberger Functional Equations to enumerate (in Polynomial Time!) Generalized Wilf classes
Brian Nakamura, Doron Zeilberger
One of the most challenging problems in enumerative combinatorics is to count Wilf classes, where you are given a pattern, or set of patterns, and you are asked to find a "formula"…
Computational Approaches to Consecutive Pattern Avoidance in Permutations
Brian Nakamura
In recent years, there has been increasing interest in consecutive pattern avoidance in permutations. In this paper, we introduce two approaches to counting permutations that avoid…