Zobrazeno 1 - 10
of 222
pro vyhledávání: '"Bóna, Miklós"'
Autor:
Bona, Miklos, Pittel, Boris
We find exact and asymptotic formulas for the number of pairs $(p,q)$ of $N$-cycles such that the all cycles of the product $p\cdot q$ have lengths from a given integer set. We then apply these results to prove a surprisingly high lower bound for the
Externí odkaz:
http://arxiv.org/abs/2407.10024
We call a pair of vertex-disjoint, induced subtrees of a rooted trees twins if they have the same counts of vertices by out-degrees. The likely maximum size of twins in a uniformly random, rooted Cayley tree of size $n\to\infty$ is studied. It is sho
Externí odkaz:
http://arxiv.org/abs/2312.01190
Autor:
Bona, Miklos
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, vol. 26:1, Permutation Patterns 2023, Special issues (August 21, 2024) dmtcs:12539
We use a recent result of Alin Bostan to prove that the generating functions of two infinite sequences of permutation classes are not algebraic.
Comment: 9 pages
Comment: 9 pages
Externí odkaz:
http://arxiv.org/abs/2310.13649
Autor:
Bóna, Miklós, Dimitrov, Stoyan, Labelle, Gilbert, Li, Yifei, Pappe, Joseph, Vindas-Meléndez, Andrés R., Zhuang, Yan
We investigate a tantalizing symmetry on Catalan objects. In terms of Dyck paths, this symmetry is interpreted in the following way: if $w_{n,k,m}$ is the number of Dyck paths of semilength $n$ with $k$ occurrences of $UD$ and $m$ occurrences of $UUD
Externí odkaz:
http://arxiv.org/abs/2212.10586
Autor:
Bóna, Miklós, Martin, Ryan R.
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 of width at most 4.
Comment: 10 pages
Comment: 10 pages
Externí odkaz:
http://arxiv.org/abs/2205.15378
Autor:
Bona, Miklos
We complete the proof of the fact that all principal permutation classes generated by a pattern longer than two have a nonrational generating function.
Comment: The proof of one crucial result needs extra work
Comment: The proof of one crucial result needs extra work
Externí odkaz:
http://arxiv.org/abs/2203.11916
Autor:
Bóna, Miklós, Pittel, Boris
We prove that for any fixed $k$, the probability that a random vertex of a random increasing plane tree is of rank $k$, that is, the probability that a random vertex is at distance $k$ from the leaves, converges to a constant $c_k$ as the size $n$ of
Externí odkaz:
http://arxiv.org/abs/2108.04989
Autor:
Bóna, Miklós, Pantone, Jay
We enumerate permutations that avoid all but one of the $k$ patterns of length $k$ starting with a monotone increasing subsequence of length $k-1$. We compare the size of such permutation classes to the size of the class of permutations avoiding the
Externí odkaz:
http://arxiv.org/abs/2103.06918
Autor:
Bóna, Miklós, Burstein, Alexander
We construct an injection from the set of permutations of length $n$ that contain exactly one copy of the decreasing pattern of length $k$ to the set of permutations of length $n+2$ that avoid that pattern. We then prove that the generating function
Externí odkaz:
http://arxiv.org/abs/2101.00332