Results 21 to 30 of about 7,280 (257)
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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The Number of Prime Parking Functions
The Mathematical Intelligencer, 2023 A parking function of length $n$ is prime if we obtain a parking function of length $n-1$ by deleting one 1 from it. In this note we give a new direct proof that the number of prime parking functions of length $n$ is $(n-1)^{n-1}$. This proof leads to a new interpretation, in close terms to the definition of parking function.
Duarte, Rui +1 more
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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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On Flattened Parking Functions
, 2022 34 pages, two tables, appeared in the Journal of Integer ...
Elder, Jennifer +4 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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Transport Automation in Urban Mobility: A Case Study of an Autonomous Parking System
Vehicles, 2022 Parking road vehicles is one of the most tedious and challenging tasks a human driver performs. Despite the low speeds involved, parking manoeuvres are among the main causes of minor and sometimes major traffic accidents, especially in urban areas where ...
Jiri Plihal +4 more
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Counting Defective Parking Functions [PDF]
The Electronic Journal of Combinatorics, 2008 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.
Cameron, P. +3 more
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Probabilizing parking functions
Advances in Applied Mathematics, 2017 We explore the link between combinatorics and probability generated by the question "What does a random parking function look like?" This gives rise to novel probabilistic interpretations of some elegant, known generating functions. It leads to new combinatorics: how many parking functions begin with $i$?
Persi Diaconis, Angela Hicks
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Extending the parking space [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 The action of the symmetric group $S_n$ on the set $\mathrm{Park}_n$ of parking functions of size $n$ has received a great deal of attention in algebraic combinatorics.
Andrew Berget, Brendon Rhoades
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An explicit formula for ndinv, a new statistic for two-shuffle parking functions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 In a recent paper, Duane, Garsia, and Zabrocki introduced a new statistic, "ndinv'', on a family of parking functions. The definition was guided by a recursion satisfied by the polynomial $\langle\Delta_{h_m}C_p1C_p2...C_{pk}1,e_n\rangle$, for $\Delta_ ...
Angela Hicks, Yeonkyung Kim
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