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 Z n -invariant d-partitions of Z n . This implies that zero-dimensional tropical ideals of degree 3 with Boolean coefficients are in bijection with Z n -invariant 2-partitions of quotient groups of the form 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 zerodimensional tropical ideals. Data Availability Statement. Data sharing not applicable to this article as no datasets were generated or analysed during the current study.
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