Results 11 to 20 of about 7,280 (257)
Symmetries in trees and parking functions
Discrete Mathematics, 2002 The author gives two new proofs of the following fact first discovered by Gessel: in the set of rooted labeled trees of \(n+1\) vertices rooted at the smallest vertex, the number of trees with \(a\) descents and \(b+1\) leaves equals the number of trees with \(b\) descents and \(a+1\) leaves (a descent is a vertex whose label is greater than at least ...
exaly +2 more sources
Probabilistic Parking Functions
The Electronic Journal of Combinatorics, 2023 We consider the notion of classical parking functions by introducing randomness and a new parking protocol, as inspired by the work presented in the paper ``Parking Functions: Choose your own adventure,'' (arXiv:2001.04817) by Carlson, Christensen, Harris, Jones, and Rodríguez.
Irfan Durmic +4 more
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Advances in Applied Mathematics, 2021 Interval parking functions (IPFs) are a generalization of ordinary parking functions in which each car is willing to park only in a fixed interval of spaces. Each interval parking function can be expressed as a pair $(a,b)$, where $a$ is a parking function and $b$ is a dual parking function. We say that a pair of permutations $(x,y)$ is \emph{reachable}
Emma Colaric +3 more
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Partial parking functions [PDF]
Discrete Mathematics, 2019 11 pages.
Rui Duarte, António Guedes de Oliveira
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Polynomials and Parking Functions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 In a 2010 paper Haglund, Morse, and Zabrocki studied the family of polynomials $\nabla C_{p1}\dots C_{pk}1$ , where $p=(p_1,\ldots,p_k)$ is a composition, $\nabla$ is the Bergeron-Garsia Macdonald operator and the $C_\alpha$ are certain slightly modified
Angela Hicks
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Special Cases of the Parking Functions Conjecture and Upper-Triangular Matrices [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 We examine the $q=1$ and $t=0$ special cases of the parking functions conjecture. The parking functions conjecture states that the Hilbert series for the space of diagonal harmonics is equal to the bivariate generating function of $area$ and $dinv$ over ...
Paul Levande
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Standard fillings to parking functions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 The Hilbert series of the Garsia-Haiman module can be written as a generating function of standard fillings of Ferrers diagrams. It is conjectured by Haglund and Loehr that the Hilbert series of the diagonal harmonics can be written as a generating ...
Elizabeth Niese
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Accurate Guidance Method and App Development for Assigning Parking Spaces Based on Indoor Wi-Fi
Promet (Zagreb), 2021 Existing parking guidance systems only provide road guidance outside the parking lot but do not provide accurate guidance to specific parking spaces inside the parking lot.
Fuquan Pan +5 more
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Affine permutations and rational slope parking functions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We introduce a new approach to the enumeration of rational slope parking functions with respect to the area and a generalized dinv statistics, and relate the combinatorics of parking functions to that of affine permutations. We relate our construction to
Eugene Gorsky +2 more
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Generalizing Parking Functions with Randomness
The Electronic Journal of Combinatorics, 2022 Consider $n$ cars $C_1, C_2, \ldots, C_n$ that want to park in a parking lot with parking spaces $1,2,\ldots,n$ that appear in order. Each car $C_i$ has a parking preference $\alpha_i \in \{1,2,\ldots,n\}$. The cars appear in order, if their preferred parking spot is not taken, they take it, if the parking spot is taken, they move forward until they ...
Melanie Tian, Enrique Treviño
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