Zobrazeno 1 - 10
of 261
pro vyhledávání: '"Pittel, Boris"'
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
Autor:
Pittel, Boris
Colloquially, there are two groups, $n$ men and $n$ women, each man (woman) ranking women (men) as potential marriage partners. A complete matching is called stable if no unmatched pair prefer each other to their partners in the matching. If some pai
Externí odkaz:
http://arxiv.org/abs/2406.10319
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:
Pittel, Boris
We study the distribution of the number of leaves of the subtree chosen uniformly at random among all the subtrees of the critical branching process tree at extinction.
Externí odkaz:
http://arxiv.org/abs/2305.03690
Autor:
Aldous, David, Pittel, Boris
In the critical beta-splitting model of a random $n$-leaf binary tree, leaf-sets are recursively split into subsets, and a set of $m$ leaves is split into subsets containing $i$ and $m-i$ leaves with probabilities proportional to $1/{i(m-i)}$. We stu
Externí odkaz:
http://arxiv.org/abs/2302.05066
Autor:
Pittel, Boris
Let $X_1,\dots, X_n$ be independent integers distributed uniformly on $\{1,\dots, M\}$, $M=M(n)\to\infty$ however slow. A partition $S$ of $[n]$ into $\nu$ non-empty subsets $S_1,\dots, S_{\nu}$ is called perfect, if all $\nu$ values $\sum_{j\in S_{\
Externí odkaz:
http://arxiv.org/abs/2210.00656
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:
Pittel, Boris
Consider a rooted tree $T$ with leaf-set $[n]$, and with all non-leaf vertices having out-degree $2$, at least. A rooted tree $\mathcal T$ with leaf-set $S\subset [n]$ is induced by $S$ in $T$ if $\mathcal T$ is the lowest common ancestor subtree for
Externí odkaz:
http://arxiv.org/abs/2102.05852
Autor:
Pittel, Boris
For a two-sided ($n$ men/$n$ women) stable matching problem) Gale and Shapley studied a proposal algorithm (men propose/women select, or the other way around), that determines a matching, not blocked by any unmatched pair. Irving used this algorithm
Externí odkaz:
http://arxiv.org/abs/2005.06691
Autor:
Pittel, Boris
Consider a cyclically ordered collection of $r$ equinumerous agent sets with strict preferences of every agent over the agents from the next agent set. A weakly stable cyclic matching is a partition of the set of agents into disjoint union of $r$-lon
Externí odkaz:
http://arxiv.org/abs/1911.07425