Plethysm and lattice point counting

摘要: We apply lattice point counting methods to compute the multiplicities in plethysm of $GL(n)$. Our approach gives insight into asymptotic growth and makes problem amenable computer algebra. prove an old conjecture Howe on leading term plethysm. For any partition $\mu$ 3,4, or 5 we obtain explicit formula $\lambda$ $k$ for multiplicity $S^\lambda$ $S^\mu(S^k)$.