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- W2998686052 abstract "We compute the type (maximum linearization) of the well partial order of bounded lower sets in $mathbb{N}^m$, ordered under inclusion, and find it is $omega^{omega^{m-1}}$; we give two proofs of this statement. Moreover we compute the type of the set of all lower sets in $mathbb{N}^m$, a topic studied by Aschenbrenner and Pong, and find that it is equal to [ omega^{sum_{k=1}^{m} omega^{m-k}binom{m}{k-1} }+ 1. ] As a consequence we deduce corresponding bounds on sequences of monomial ideals." @default.
- W2998686052 created "2020-01-10" @default.
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- W2998686052 date "2019-09-15" @default.
- W2998686052 modified "2023-09-27" @default.
- W2998686052 title "Maximum linearizations of lower sets in $mathbb{N}^m$ with application to monomial ideals" @default.
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