The Defective Parking Space and Defective Kreweras Numbers
Rebecca E. Garcia, Pamela E. Harris, Alex Moon, Aaron Ortiz, Lauren J. Quesada, Cynthia Marie Rivera S\'anchez, Dwight Anderson Williams II, Alexander N. Wilson

TL;DR
This paper introduces defective parking functions and spaces, explores their symmetry properties, and connects them to Young tableaux and Kreweras numbers, providing formulas for counting and characterizing these structures.
Contribution
It defines defective parking functions and spaces, establishes their symmetry invariance, and links them to Young tableaux and Kreweras numbers, including conjectured formulas and counting methods.
Findings
Defective parking functions are invariant under symmetric group actions.
The set of nondecreasing defective parking functions corresponds to Young tableaux of specific shapes.
New formulas for counting defective parking functions and their orbits are derived.
Abstract
A defective -parking function with defect is a parking function with cars attempting to park on a street with parking spots in which exactly cars fail to park. We establish a way to compute the defect of a defective -parking function and show that the defect of a parking function is invariant under the action of , the symmetric group on . We introduce the defective parking space spanned by defective parking functions and describe its Frobenius characteristic as an representation graded by defect via coefficients called defective Kreweras numbers. We provide a conjectured formula for for sufficiently large . We also show that the set of nondecreasing defective -parking functions with defect are in bijection…
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Taxonomy
TopicsSmart Parking Systems Research
