Claudia Andrei-Ciobanu: Kruskal-Katona theorem for $t$-spread strongly stable ideals, 107-122

Abstract:

We prove that any $t$-spread strongly stable ideal has a unique $t$-spread lex ideal with the same $f_t$-vector. We also characterize the possible $f_t$-vectors of $t$-spread strongly stable ideals in the "$t$-spread" analogue of Kruskal-Katona theorem.

Key Words: t-spread strongly stable ideals, Stanley-Reisner ideals, Kruskal-Katona Theorem, Hilbert series.

2010 Mathematics Subject Classification: Primary 05E40; Secondary 13A02, 13D40, 13F55.