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A sequence $(e_1,e_2,\\ldots,e_n)$ of nonnegative integers is called an $s$-inversion sequence of length $n$ if $0\\leq e_i < s_i$ for $1\\leq i\\leq n$. Let I(n) be the set of $s$-inversion sequences of length $n$ for $s=(1,4,3,8,5,12,\\ldots)$, that is, $s_{2i}=4i$ and $s_{2i-1}=2i-1$ for $i\\geq1$, and let $P_n$ be the set of signed permutations on $\\{1^2,2^2,\\ldots,n^2\\}$. 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Guo, Harry H.Y. Huang, Peter L. Guo, Thomas Y.H. Liu, William Y.C. Chen","submitted_at":"2013-10-20T09:34:00Z","abstract_excerpt":"Given a sequence $s=(s_1,s_2,\\ldots)$ of positive integers, the inversion sequences with respect to $s$, or $s$-inversion sequences, were introduced by Savage and Schuster in their study of lecture hall polytopes. A sequence $(e_1,e_2,\\ldots,e_n)$ of nonnegative integers is called an $s$-inversion sequence of length $n$ if $0\\leq e_i < s_i$ for $1\\leq i\\leq n$. Let I(n) be the set of $s$-inversion sequences of length $n$ for $s=(1,4,3,8,5,12,\\ldots)$, that is, $s_{2i}=4i$ and $s_{2i-1}=2i-1$ for $i\\geq1$, and let $P_n$ be the set of signed permutations on $\\{1^2,2^2,\\ldots,n^2\\}$. 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