Related papers: Probabilizing Parking Functions
Noting a curious link between Andrews' even-odd crank and the Stanley rank, we adopt a combinatorial approach building on the map of conjugation and continue the study of integer partitions with parts separated by parity. Our motivation is…
Different steps leading to the new functional for pairing based on natural orbitals and occupancies proposed in ref. [D. Lacroix and G. Hupin, arXiv:1003.2860] are carefully analyzed. Properties of quasi-particle states projected onto good…
We give a formula for the bivariate generating function of a stationary 1-dependent counting process in terms of its run probability generating function, with a probabilistic proof. The formula reduces to the well known bivariate generating…
We introduce a new parking procedure called MVP parking in which $n$ cars sequentially enter a one-way street with a preferred parking spot from the $n$ parking spots on the street. If their preferred spot is empty, they park there.…
In this paper, cylindric partitions into profiles $c=(1,1)$ and $c=(2,0)$ are considered. The generating functions into unrestricted cylindric partitions and cylindric partitions into distinct parts with these profiles are constructed. The…
Let $W$ be a Weyl group with root lattice $Q$ and Coxeter number $h$. The elements of the finite torus $Q/(h+1)Q$ are called the $W$-{\sf parking functions}, and we call the permutation representation of $W$ on the set of $W$-parking…
We study the problem of enumerating answers of Conjunctive Queries ranked according to a given ranking function. Our main contribution is a novel algorithm with small preprocessing time, logarithmic delay, and non-trivial space usage during…
This work is a numerical experiment of stochastic motion of conservative Hamiltonian system or weakly damped Brownian particles. The objective is to prove the existence of path probability and to compute its values. By observing a large…
We study generating functions of ordinary and plane partitions coloured by the action of a finite subgroup of the corresponding special linear group. After reviewing known results for the case of ordinary partitions, we formulate a…
Recently, the authors extended the notion of parking functions to parking sequences, which include cars of different sizes, and proved a product formula for the number of such sequences. We here give a refinement of that result involving…
In this research, Minkowski type functions which are constructed on certain probability distributions, are introduced. There are investigated differential, integral, and other properties of these functions.
In this short article, we will focus on the different links between some stochastic processes resulting from Brownian motion and two notions of probability theory (proportional increments and last hitting times).
In this work we define a unified generating functions for 9 different kinds of set partitions including cyclically ordered set partitions. Such generating function depends on 4 parameters. We consider property of this function and provide…
Functional equations (FE) arise quite naturally in the analysis of stochastic systems of different kinds : queueing and telecommunication networks, random walks, enumeration of planar lattice walks, etc. Frequently, the object is to…
We find generating functions the number of strings (words) containing a specified number of occurrences of certain types of order-isomorphic classes of substrings called subword patterns. In particular, we find generating functions for the…
Adding a column of numbers produces "carries" along the way. We show that random digits produce a pattern of carries with a neat probabilistic description: the carries form a one-dependent determinantal point process. This makes it easy to…
There is a close connection between intersections of Brownian motion paths and percolation on trees. Recently, ideas from probability on trees were an important component of the multifractal analysis of Brownian occupation measure, in joint…
We formulate some problems and conjectures about semigroups of rational functions under composition. The considered problems arise in different contexts, but most of them are united by a certain relationship to the concept of amenability.
Stanley recently introduced the shifted parking function symmetric function $SH_n$, which is the shiftification of Haiman's parking function symmetric function $PF_n$. The function $SH_n$ lives in the subalgebra of symmetric functions…
We consider the variance of sums of arithmetic functions over random short intervals in the function field setting. Based on the analogy between factorizations of random elements of $\mathbb{F}_q[T]$ into primes and the factorizations of…