Freiman $t$-spread principal Borel ideals

Abstract

where ℓ(I) is the analytic spread of I and µ(I) is the least number of monomial generators of I. Freiman ideals are special since there exists an exact formula computing the least number of monomial generators of any of their powers. In this paper we give a complete classification of Freiman t-spread principal Borel ideals.

Freiman Borel type ideals

“…If k = 1, then B k (u) is a 1-spread Borel ideal. In this case, a complete classification has been given in [18]. Next, we only focus on the cases k = d − 1 and k = 2.…”

“…This is a very restrictive condition for ideals arising from combinatorial structures, which often guarantees strong combinatorial properties. Many classes of Freiman ideals such as Hibi ideals, Veronese type ideals, matroid ideals, sortable ideals, principal Borel ideals, t-spread principal Borel ideals, edge ideals and cut ideals of several graphs, and cover ideals of some classes of graphs such as trees, circulant graphs, whiskered graphs and simple connected unmixed bipartite graphs have been studied (see [6,14,15,16,17,18]).…”

“…If k = 1, then B k (u) is a 1-spread Borel ideal. In this case, a complete classification has been given in [18]. We provide a complete classification of Freiman principal k-Borel ideals of degree…”