266 citations · 723 across the 48 of their papers we have counts for
6 papers · 1 filter
On the Best Upper Bound for Permutations Avoiding A Pattern of a Given Length
Miklos Bona
Numerical evidence suggests that certain permutation patterns of length k are easier to avoid than any other patterns of that same length. We prove that these patterns are avoided…
A new upper bound for 1324-avoiding permutations
Miklos Bona
We prove that the number of 1324-avoiding permutations of length n is less than (7+4\sqrt{3})^n.
On a Family of Conjectures of Joel Lewis on Alternating Permutations
Miklos Bona
We prove generalized versions of some conjectures of Joel Lewis on the number of alternating permutations avoiding certain patterns. Our main tool is the perhaps surprising observa…
The Number of Ways to Assemble a Graph
Andrew Vince, Miklos Bona
Motivated by the question of how macromolecules assemble, the notion of an {\it assembly tree} of a graph is introduced. Given a graph , the paper is concerned with enumerating…
A Bijective Proof of and Identity Extending a Classic Result of Hajos
Miklos Bona
We provide bijective proofs of two classic identities that are very simple to prove using generating functions, but surprisingly difficult to prove combinatorially. The problem of…
Surprising symmetries in 132-avoiding permutations
Miklos Bona
We prove that the total number of copies of the pattern in all 132-avoiding permutations of length is the same for , , or . We provide a…