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Improved Immune Moth–Flame Algorithm for Intelligent Vehicle Parking Path Optimization [PDF]
BiomimeticsIntelligent parking systems have been recognized as a core technological intervention for resolving parking garage shortages and advancing traffic safety. Nevertheless, it remains challenging to generate a smooth, accurate, and optimal parking trajectory
Yan Chen +3 more
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A further correspondence between $(bc,\bar{b})$-parking functions and $(bc,\bar{b})$-forests [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 For a fixed sequence of $n$ positive integers $(a,\bar{b}) := (a, b, b,\ldots, b)$, an $(a,\bar{b})$-parking function of length $n$ is a sequence $(p_1, p_2, \ldots, p_n)$ of positive integers whose nondecreasing rearrangement $q_1 \leq q_2 \leq \cdots ...
Heesung Shin, Jiang Zeng
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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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Hyperplane Arrangements and Diagonal Harmonics [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 In 2003, Haglund's bounce statistic gave the first combinatorial interpretation of the q,t-Catalan numbers and the Hilbert series of diagonal harmonics. In this paper we propose a new combinatorial interpretation in terms of the affine Weyl group of type
Drew Armstrong
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Interval and $\ell$-interval Rational Parking Functions [PDF]
Discrete Mathematics & Theoretical Computer ScienceInterval parking functions are a generalization of parking functions in which cars have an interval preference for their parking. We generalize this definition to parking functions with $n$ cars and $m\geq n$ parking spots, which we call interval ...
Tomás Aguilar-Fraga +14 more
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Two special cases of the Rational Shuffle Conjecture [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 The Classical Shuffle Conjecture of Haglund et al. (2005) has a symmetric function side and a combinatorial side. The combinatorial side $q,t$-enumerates parking functions in the $n ×n$ lattice.
Emily Leven
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