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- W2077550488 abstract "Let $alpha$ be a string over $mathbb{Z}_p$ with p prime. The jth elementary symmetric function evaluated at $alpha$ is denoted $T_j(alpha)$. We study the cardinalities $S_p(n;tau_1,tau_2,ldots,tau_t)$ of the set of length n strings for which $T_i(alpha) = tau_i$. The emph{profile} $langle k_0,k_1,ldots,k_{p-1} rangle$ of a string $alpha$ is the sequence of frequencies with which each letter occurs. The profile of $alpha$ determines $T_j(alpha)$, and hence $S_p$. Let $f_n : mathbb{Z}_{p^n}^{p-1} mapstonobreak mathbb{Z}_p^{p^n-1}$ be the map that takes $langle k_0,k_1,ldots,k_{p-1} rangle bmod {p^n}$ to $(T_1,T_2,ldots,T_{p^n-1}) bmod p$. We show that $f_n$ is well defined and injective and show how to efficiently determine its range. These results are used to efficiently compute $S_p(n;tau_1,tau_2,ldots,tau_t)$." @default.
- W2077550488 created "2016-06-24" @default.
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- W2077550488 date "2004-01-01" @default.
- W2077550488 modified "2023-09-26" @default.
- W2077550488 title "Counting Strings with Given Elementary Symmetric Function Evaluations I: Strings over boldmath$mathbbZ_p$ withpPrime" @default.
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- W2077550488 doi "https://doi.org/10.1137/s0895480102415381" @default.
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