2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75914A short new proof of the fact that all shifted complexes are fixed by reverse lexicographic shifting is given. A notion of lexicographic shifting, $Δ_{\lex}$ -- an operation that transforms a monomial ideal of $S=\field[x_i: i\in\N]$ that is finitely generated in each degree into a squarefree strongly stable ideal -- is defined and studied. It is proved that (in contrast to the reverse lexicographic case) a squarefree strongly stable ideal $I\subset S$ is fixed by lexicographic shifting if and only if $I$ is a universal squarefree lexsegment ideal (abbreviated USLI) of $S$. Moreover, in the case when $I$ is finitely generated and is not a USLI, it is verified that all the ideals in the sequence $\{Δ_{\lex}^i(I)\}_{i=0}^{\infty}$ are distinct. The limit ideal $\barΔ(I)=\lim_{i\to\infty}Δ_{\lex}^i(I)$ is well defined and is a USLI that depends only on a certain analog of the Hilbert function of $I$.to appear in the Journal of Algebraic CombinatoricsCombinatoricsCommutative Algebra05E02, 13C02text