Related papers: Foata, Hikita, and the Bulldozer Problem

In recent work, we considered the frequencies of patterns of consecutive primes $\pmod{q}$ and numerically found biases toward certain patterns and against others. We made a conjecture explaining these biases, the dominant factor in which…

Possibility and probability theories are alternative and complementary ways to deal with uncertainty, which has motivated over the last years an interest for the study of ways to transform probability distributions into possibility…

We shift the perspective on the interval fragmentation problem from division points to division spacings. This leads to a proof that is both simpler and stronger, establishing limiting distributions for partition points and spacings and,…

Liu and Liu in 2007 introduced the Fourier - Hermite transform $\sum a_{n}\lambda_{n}^{R}\psi_{n}(t)$ which is a random Fourier - Hermite series with random variables $\lambda_{n}^{R}$ choosen randomly from the unit circle of $\mathbb{C}$,…

Probabilistic models for the distribution of primes in the natural numbers are constructed in the article. The author found and proved the probabilistic estimates of the deviation $R(x)=|\pi(x)- Li(x)|$. The author has analyzed the…

Let $\eta_i, i=1,..., n$ be iid Bernoulli random variables, taking values $\pm 1$ with probability 1/2. Given a multiset $V$ of $n$ elements $v_1, ..., v_n$ of an additive group $G$, we define the \emph{concentration probability} of $V$ as…

We analyze here in details the probability to find a given number of particles in a finite volume inside a normal or superfluid finite system. This probability, also known as counting statistics, is obtained using projection operator…

In [3], we have introduced a probability measure to study the power and exponential sums for a certain coding system. The distribution function of the probability measure gives explicit formulas for the power and exponential sums.…

The authors present a new simple algorithm to approximate weakly stochastic differential equations in the spirit of [1] and [2]. They apply it to the problem of pricing Asian options under the Heston stochastic volatility model, and compare…

Buryak, Feigin and Nakajima computed a generating function for a family of partition statistics by using the geometry of the $Z/cZ$ fixed point sets in the Hilbert scheme of points on $C^2$. Loehr and Warrington had already shown how a…

Drawing on a problem posed by Hertzsprung in 1887, we say that a given permutation $\pi\in\mathcal{S}_n$ contains the Hertzsprung pattern $\sigma\in\mathcal{S}_k$ if there is factor $\pi(d+1)\pi(d+2)\cdots\pi(d+k)$ of $\pi$ such that…

We present a new distributed fuzzy partitioning method to reduce the complexity of multi-way fuzzy decision trees in Big Data classification problems. The proposed algorithm builds a fixed number of fuzzy sets for all variables and adjusts…

The theory of equidistribution is about hundred years old, and has been developed primarily by number theorists and theoretical computer scientists. A motivated uninitiated peer could encounter difficulties perusing the literature, due to…

The well-known Hardy--Ramanujan inequality states that if $\omega(n)$ denotes the number of distinct prime factors of a positive integer $n$, then there is an absolute constant $C>0$ such that uniformly for $x\ge2$ and $k\in\mathbb{N}$,…

Babson and Steingr\'{\i}msson introduced generalized permutation patterns and showed that most of the Mahonian statistics in the literature can be expressed by the combination of generalized pattern functions. Particularly, they defined a…

Let us consider i.i.d. random variables $\{a_k,b_k\}_{k \geq 1}$ defined on a common probability space $(\Omega, \mathcal F, \mathbb P)$, following a symmetric Rademacher distribution and the associated random trigonometric polynomials…

We study several stochastic combinatorial problems, including the expected utility maximization problem, the stochastic knapsack problem and the stochastic bin packing problem. A common technical challenge in these problems is to optimize…

We find a new obstruction to the existence of solutions of the Hull-Strominger system, which goes beyond the balanced property of the Calabi-Yau manifold $(X,\Omega)$ and the Mumford-Takemoto slope stability of the bundle over it. The basic…

In symmetric groups, studies of permutation factorizations or triples of permutations satisfying certain conditions have a long history. One particular interesting case is when two of the involved permutations are long cycles, for which…

A stochastic hybrid system, also known as a switching diffusion, is a continuous-time Markov process with state space consisting of discrete and continuous parts. We consider parametric estimation of theQmatrix for the discrete state…