Boij–Söderberg decompositions of lexicographic ideals

Boij–Söderberg theory describes the Betti diagrams of graded modules over a polynomial ring as a linear combination of pure diagrams with positive coefficients. In this paper, we focus on the Betti diagrams of lexicographic ideals. Mainly, we characterize the Boij–Söderberg decomposition of the Betti table of a lexicographic ideal in the polynomial ring with three variables, and show a nice connection between its Boij–Söderberg decomposition and the ones of other related lexicographic ideals.