Related papers: Preference-restricted parking functions
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…
A supervised learning algorithm searches over a set of functions $A \to B$ parametrised by a space $P$ to find the best approximation to some ideal function $f\colon A \to B$. It does this by taking examples $(a,f(a)) \in A\times B$, and…
We develop a new closed-form arithmetic and recursive formula for the partition function and a generalization of Andrews' smallest parts (spt) function. Using the inclusion-exclusion principle, we additionally develop a formula for the…
To gain theoretical insight into the relationship between parking scarcity and congestion, we describe block-faces of curbside parking as a network of queues. Due to the nature of this network, canonical queueing network results are not…
For a directed graph G on vertices {0,1,...,n}, a G-parking function is an n-tuple (b_1,...,b_n) of non-negative integers such that, for every non-empty subset U of {1,...,n}, there exists a vertex j in U for which there are more than b_j…
In this paper, we introduce a new variant of the $p$-median facility location problem in which it is assumed that the exact location of the potential facilities is unknown. Instead, each of the facilities must be located in a region around…
Intrinsic location functional is a large class of random locations containing locations that one may encounter in many cases, e.g., the location of the path supremum/infimum over a given interval, the first/last hitting time, etc. It has…
Binary functions are a generalisation of the cocircuit spaces of binary matroids to arbitrary functions. Every rank function is assigned a binary function, and the deletion and contraction operations of binary functions generalise matroid…
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…
Probability functions appear in constraints of many optimization problems in practice and have become quite popular. Understanding their first-order properties has proven useful, not only theoretically but also in implementable algorithms,…
In this paper, a new formula for {\pi}^(2)(N) is formulated, it is a function that counts the number of semi-primes not exceeding a given number N. A semi-prime is a natural number that is the product of precisely two prime numbers, the two…
The unit selection problem is to identify a group of individuals who are most likely to exhibit a desired mode of behavior, for example, selecting individuals who would respond one way if incentivized and a different way if not. The unit…
We study lucky cars in subsets of parking functions, called Fubini rankings and unit Fubini rankings. A Fubini ranking is a sequence of nonnegative integers that encodes a valid ranking of competitors, where ties are allowed. A car (or…
We show that a minimal triangulation of the associahedron (Stasheff polytope) of dimension n is made of (n+1)^{n-1} simplices. We construct a natural bijection with the set of parking functions from a new interpretation of parking functions…
A ridge function is a function of several variables that is constant along certain directions in its domain. Using classical dimensional analysis, we show that many physical laws are ridge functions; this fact yields insight into the…
We give an exact enumerative formula for the minimal acyclic deterministic finite automata. This formula is obtained from a bijection between a family of generalized parking functions and the transitions functions of acyclic automata.
Multi-task learning aims to acquire a set of functions, either regressors or classifiers, that perform well for diverse tasks. At its core, the idea behind multi-task learning is to exploit the intrinsic similarity across data sources to…
Preference-based learning of reward functions, where the reward function is learned using comparison data, has been well studied for complex robotic tasks such as autonomous driving. Existing algorithms have focused on learning reward…
Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in…
Place a car independently with probability $p$ at each site of a graph. Each initially vacant site is a parking spot that can fit one car. Cars simultaneously perform independent random walks. When a car encounters an available parking spot…