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- W2964154473 abstract "The partial Stirling numbers $T_n(k)$ used here are defined as $sum_{itext{ odd}}binom{n}{i}i^k$. Their 2-exponents $nu(T_n(k))$ are important in algebraic topology. We provide many specific results, applying to all values of $n$, stating that, for all $k$ in a certain congruence class mod $2^t$, $nu(T_n(k))=nu(k-k_0)+c_0$, where $k_0$ is a 2-adic integer and $c_0$ a positive integer. Our analysis involves several new general results for $nu(sumbinom{n}{2i+1}i^j)$, the proofs of which involve a new family of polynomials. Following Clarke [3], we interpret $T_n$ as a function on the 2-adic integers, and the 2-adic integers $k_0$ described above as the zeros of these functions." @default.
- W2964154473 created "2019-07-30" @default.
- W2964154473 creator A5015290951 @default.
- W2964154473 date "2013-09-01" @default.
- W2964154473 modified "2023-10-03" @default.
- W2964154473 title "Divisibility by 2 of partial Stirling numbers" @default.
- W2964154473 doi "https://doi.org/10.7169/facm/2013.49.1.2" @default.
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