2 citations · 7 across the 10 of their papers we have counts for
11 papers
On the Average Sizes of Ideals and Antichains in Some Infinite Families of Posets
Miklos Bona, Ricardo Gomez Aiza
We study the average sizes of ideals and antichains in several families of posets arising from rooted unlabeled trees. For ideals, we encode order ideals by coloring vertices red,…
Letter frequency in shifts of finite type with one forbidden word
Miklós Bóna, Balázs Maga, Jacob Richey
This work considers combinatorial and statistical aspects of {\em{shifts of finite type}}, which are families of words over a finite alphabet which avoid a fixed class of {\emph{fo…
Boolean--Eulerian numbers
Miklós Bóna, Vincent Vatter
We study decreasing binary trees in which every vertex with two children is colored red or blue. We construct two bijections. The first, to ordered set partitions into odd-sized bl…
A combinatorial proof of a symmetry for a refinement of the Narayana numbers
Miklós Bóna, Stoyan Dimitrov, Gilbert Labelle +4
We establish a tantalizing symmetry of certain numbers refining the Narayana numbers. In terms of Dyck paths, this symmetry is interpreted in the following way: if is t…
The Endomorphism Conjecture for Graded Posets of Width 4
Miklós Bóna, Ryan R. Martin
We prove the endomorphism conjecture for graded posets whose largest Whitney number is at most 4. In particular, this implies the endomorphism conjecture is true for graded posets…
Random increasing plane trees: asymptotic enumeration of vertices by distance from leaves
Miklós Bóna, Boris Pittel
We prove that for any fixed , the probability that a random vertex of a random increasing plane tree is of rank , that is, the probability that a random vertex is at distance…
Permutations avoiding sets of patterns with long monotone subsequences
Miklós Bóna, Jay Pantone
We enumerate permutations that avoid all but one of the patterns of length starting with a monotone increasing subsequence of length . We compare the size of such perm…
Permutations with exactly one copy of a decreasing pattern of length k
Miklós Bóna, Alexander Burstein
We construct an injection from the set of permutations of length that contain exactly one copy of the decreasing pattern of length to the set of permutations of length $n+2…
Generating functions of permutations with respect to their alternating runs
Miklós Bóna
We present a short, direct proof of the fact that the generating function of all permutations of a fixed length is divisible by , where $m=\lfloor (n-2)/2 \rfloo…
Most principal permutation classes have nonrational generating functions
Miklós Bóna
We prove that for any fixed , and for most permutation patterns , the number of -avoiding permutations of length that consist of skew…
Log-concavity, the Ulam distance and involutions
Miklós Bóna, Marie-Louise Bruner
We prove that in a large collection of naturally defined sets of permutations of fixed length, the numbers of permutations at Ulam distance k from the identity form a log-concave s…