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- W4206669936 abstract "Tropical ideals are a class of ideals in the tropical polynomial semiring that combinatorially abstracts the possible collections of supports of all polynomials in an ideal over a field. We study zero-dimensional tropical ideals I with Boolean coefficients in which all underlying matroids are paving matroids, or equivalently, in which all polynomials of minimal support have support of size $$deg (I)$$ or $$deg (I)+1$$ —we call them paving tropical ideals. We show that paving tropical ideals of degree $$d+1$$ are in bijection with $${mathbb {Z}}^n$$ -invariant d-partitions of $${mathbb {Z}}^n$$ . This implies that zero-dimensional tropical ideals of degree 3 with Boolean coefficients are in bijection with $${mathbb {Z}}^n$$ -invariant 2-partitions of quotient groups of the form $${mathbb {Z}}^n/L$$ . We provide several applications of these techniques, including a construction of uncountably many zero-dimensional degree-3 tropical ideals in one variable with Boolean coefficients, and new examples of non-realizable zero-dimensional tropical ideals." @default.
- W4206669936 created "2022-01-26" @default.
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- W4206669936 date "2022-01-03" @default.
- W4206669936 modified "2023-09-26" @default.
- W4206669936 title "Paving tropical ideals" @default.
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- W4206669936 doi "https://doi.org/10.1007/s10801-021-01100-3" @default.
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