Related papers: Parking functions with zero secondary dinv

Let $\mathbb{F}_q$ be a finite field of odd characteristic. We study R\'edei functions that induce permutations over $\mathbb{P}^1(\mathbb{F}_q)$ whose cycle decomposition contains only cycles of length $1$ and $j$, for an integer $j\geq…

We introduce a bijection between inequivalent minimal factorizations of the n-cycle (1 2 ... n) into a product of smaller cycles of given length, on one side, and trees of a certain structure on the other. We use this bijection to count the…

We prove that for continuous maps on the interval, the existence of an n-cycle, implies the existence of n-1 points which interwind the original ones and are permuted by the map. We then use this combinatorial result to show that piecewise…

We give new equations which characterize the generating functions of planar quadrangulations and planar triangulations, with zero, one or two boundaries. The proof is inspired by the Lackner--Panholzer last car decomposition of parking…

We show that the proportion of permutations of length $n$ with principal M\"{o}bius function equal to zero, $Z(n)$, is asymptotically bounded below by 0.3995. If a permutation $\pi$ contains two intervals of length 2, where one interval is…

Let $m, n$ be positive integers such that $m>1$ divides $n$. In this paper, we introduce a special class of piecewise-affine permutations of the finite set $[1, n]:=\{1, \ldots, n\}$ with the property that the reduction $\pmod m$ of $m$…

We present a first-order theorem proving framework for establishing the correctness of functional programs implementing sorting algorithms with recursive data structures. We formalize the semantics of recursive programs in many-sorted…

We consider a sequence $(p_n)_{n=1}^\infty$ of polynomials with uniformly bounded zeros and $\deg p_1\geq 1$, $\deg p_n\geq 2$ for $n\geq 2$, satisfying certain asymptotic conditions. We prove that the function sequence $\left(\frac{1}{\deg…

A depth-first search version of Dhar's burning algorithm is used to give a bijection between the parking functions of a graph and labeled spanning trees, relating the degree of the parking function with the number of inversions of the…

In this expository article I describe classical results in the combinatorics of parking functions. Its English-Spanish translation is included. -- -- En este art\'iculo de difusi\'on matem\'atica describo resultados cl\'asicos en la…

We introduce a basis of rational polynomial-like functions $P_0,\ldots,P_{n-1}$ for the free module of functions $Z/nZ\to Z/mZ$. We then characterize the subfamily of congruence preserving functions as the set of linear combinations of the…

We describe an algorithm, implemented in Python, which can enumerate any permutation class with polynomial enumeration from a structural description of the class. In particular, this allows us to find formulas for the number of permutations…

In this article we give an order-dividing bijective function between cyclic and non cyclic groups of finite order. In particular, we prove that there exists a bijective function from D_{2n} to Z_{2n} for any natural integer n; and from Z_p…

A special type of binomial splitting process is studied. Such a process can be used to model a high-dimensional corner parking problem, as well as the depth of random PATRICIA tries (a special class of digital tree data structures). The…

We construct iteratively a sequence of numbers k_{n} and Beurling functions A_{n} converging pointwise to -1 in [0,1]. We prove results which seems to suggest that each A_{n} is equal to a well known approximating sequence of functions…

This paper contains a partial answer to the open problem 3.11 of \cite{[H2008]}. That is to find an explicit bijection on Schr\"oder paths that inverts the statistics area and bounce. This paper started as an attempt to write the sum over…

Tiered trees were introduced as a combinatorial object for counting absolutely indecomposable representation of certain quivers and torus orbit of certain homogeneous variety. In this paper, we define a bijection between the set of…

We compute the correlation function in the equilibrium version of R\'enyi's {\sl parking problem}. The correlation length is found to diverge as $2^{-1}\pi^{-2}(1-\rho)^{-2}$ when $\rho\nearrow1$ (maximum density) and as…

We present an algorithm that generates multiset permutations in O(1) time for each permutation, that is, by a loop-less algorithm with O(n) extra memory requirement. There already exist several such algorithms that generate multiset…

For a set of nonnegative integers $A$, denote by $R_{A}(n)$ the number of unordered representations of the integer $n$ as the sum of two different terms from $A$. In this paper we partially describe the structure of the sets, which have…