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Harris, Qingzhong Liang, Steve Butler","submitted_at":"2019-12-03T21:29:14Z","abstract_excerpt":"Given a strictly increasing sequence $\\mathbf{t}$ with entries from $[n]:=\\{1,\\ldots,n\\}$, a parking completion is a sequence $\\mathbf{c}$ with $|\\mathbf{t}|+|\\mathbf{c}|=n$ and $|\\{t\\in \\mathbf{t}\\mid t\\le i\\}|+|\\{c\\in \\mathbf{c}\\mid c\\le i\\}|\\ge i$ for all $i$ in $[n]$. We can think of $\\mathbf{t}$ as a list of spots already taken in a street with $n$ parking spots and $\\mathbf{c}$ as a list of parking preferences where the $i$-th car attempts to park in the $c_i$-th spot and if not available then proceeds up the street to find the next available spot, if any. 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