Zobrazeno 1 - 10
of 27
pro vyhledávání: '"60C05, 05A16"'
The $n$ queens problem considers the maximum number of safe squares on an $n \times n$ chess board when placing $n$ queens; the answer is only known for small $n$. Miller, Sheng and Turek considered instead $n$ randomly placed rooks, proving the prop
Externí odkaz:
http://arxiv.org/abs/2409.04423
Consider a non-negative sequence $c_n = h(n) \cdot n^{\alpha-1} \cdot \rho^{-n}$, where $h$ is slowly varying, $\alpha>0$, $0<\rho<1$ and $n\in\mathbb{N}$. We investigate the coefficients of $G(x,y) = \prod_{k\ge1}(1-x^ky)^{-c_k}$, which is the bivar
Externí odkaz:
http://arxiv.org/abs/2203.15543
Autor:
Yin, Mei
Given a positive-integer-valued vector $u=(u_1, \dots, u_m)$ with $u_1<\cdots
Externí odkaz:
http://arxiv.org/abs/2112.02251
Autor:
Kenyon, Richard, Yin, Mei
Suppose that $m$ drivers each choose a preferred parking space in a linear car park with $n$ spots. In order, each driver goes to their chosen spot and parks there if possible, and otherwise takes the next available spot if it exists. If all drivers
Externí odkaz:
http://arxiv.org/abs/2103.17180
Autor:
Budzinski, Thomas, Louf, Baptiste
We study the local limits of uniform high genus bipartite maps with prescribed face degrees. We prove the convergence towards a family of infinite maps of the plane, the q-IBPMs, which exhibit both a spatial Markov property and a hyperbolic behaviour
Externí odkaz:
http://arxiv.org/abs/2012.05813
The variance of a linear statistic defined on the symmetric group endowed with the Ewens probability is examined. Despite the dependence of the summands, it can be bounded from above by a constant multiple of the sum of variances. We find the exact v
Externí odkaz:
http://arxiv.org/abs/2003.05975
We revisit the model of the ballistic deposition studied in \cite{bdeposition} and prove several combinatorial properties of the random tree structure formed by the underlying stochastic process. Our results include limit theorems for the number of r
Externí odkaz:
http://arxiv.org/abs/1903.12548
Autor:
Budzinski, Thomas, Louf, Baptiste
We prove a conjecture of Benjamini and Curien stating that the local limits of uniform random triangulations whose genus is proportional to the number of faces are the Planar Stochastic Hyperbolic Triangulations (PSHT) defined in arXiv:1401.3297. The
Externí odkaz:
http://arxiv.org/abs/1902.00492
Autor:
Handelman, David
The following class of problems arose out of vain attempts to show that the Pascal's triangle adic transformation has trivial spectrum. Partition a set of size $N$ into sets of size $S \equiv S(N)$ (ignoring leftovers). What is the likelihood that a
Externí odkaz:
http://arxiv.org/abs/1608.07635
Publikováno v:
SIAM J. Discrete Math. 29 (2015), no. 3, 1600-1653
For fixed $t\ge 2$, we consider the class of representations of $1$ as sum of unit fractions whose denominators are powers of $t$ or equivalently the class of canonical compact $t$-ary Huffman codes or equivalently rooted $t$-ary plane "canonical" tr
Externí odkaz:
http://arxiv.org/abs/1503.08791