منابع مشابه
On the Enumeration of Generalized Parking Functions
Let x = (x1, x2, . . . , xn) ∈ Nn . Define a x-parking function to be a sequence (a1, a2, . . . , an) of positive integers whose non-decreasing rearrangement b1 ≤ b2 ≤ · · · ≤ bn satisfies bi ≤ x1+ · · ·+xi. Let Pn(x) denote the number of x-parking functions. We discuss the enumerations of such generalized parking functions. In particular, We give the explicit formulas and present two proofs, o...
متن کاملCounting Defective Parking Functions
Suppose that m drivers each choose a preferred parking space in a linear car park with n spaces. Each driver goes to the chosen space and parks there if it is free, and otherwise takes the first available space with a larger number (if any). If all drivers park successfully, the sequence of choices is called a parking function. In general, if k drivers fail to park, we have a defective parking ...
متن کاملGenomes and Parking Functions
This paper will focus on rearrangements of genomes containing linear chromosomes. The goal is to be able to be able to enumerate thee rearrangements. This will be done first by determining the number of operations required to rearrange one genome into another. Then if the order in which these operations occur can be altered, the resulting effects on the enumeration will be determined. We will b...
متن کاملSome Enumerations for Parking Functions
In this paper, let Pn,n+k;≤n+k (resp. Pn;≤s) denote the set of parking functions α = (a1, · · · , an) of length n with n+k (respe. n)parking spaces satisfying 1 ≤ ai ≤ n+k (resp. 1 ≤ ai ≤ s) for all i. Let pn,n+k;≤n+k = |Pn,n+k;≤n+k| and pn;≤s = |Pn;≤s|. Let P l n;≤s denote the set of parking functions α = (a1, · · · , an) ∈ Pn;≤s such that a1 = l and pn;≤s = |P l n;≤s|. We derive some formulas...
متن کاملParking Functions and Descent Algebras
We show that the notion of parkization of a word, a variant of the classical standardization, allows to introduce an internal product on the Hopf algebra of parking functions. Its Catalan subalgebra is stable under this operation and contains the descent algebra as a left ideal.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2002
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(02)00338-2