1,372 research outputs found
The stable set of associated prime ideals of a squarefree principal Borel ideal
It is shown that a squarefree principal Borel ideal satisfies the persistence
property for the associated prime ideals. For the graded maximal ideal we
compute the index of stability with respect to squarefree principal Borel
ideals and determine their stable set of associated prime ideals
Toric ideals associated with gap-free graphs
In this article we prove that every toric ideal associated with a gap-free
graph has a squarefree lexicographic initial ideal. Moreover, in the
particular case when the complementary graph of is chordal (i.e. when the
edge ideal of has a linear resolution), we show that there exists a reduced
Gr\"obner basis of the toric ideal of such that all the
monomials in the support of are squarefree. Finally, we show
(using work by Herzog and Hibi) that if is a monomial ideal generated in
degree 2, then has a linear resolution if and only if all powers of
have linear quotients, thus extending a result by Herzog, Hibi and Zheng.Comment: 13 pages, v2. To appear in Journal of Pure and Applied Algebr
On infinite words avoiding a finite set of squares
Building an infinite square-free word by appending one letter at a time while
simultaneously avoiding the creation of squares is most likely to fail. When
the alphabet has two letters this approach is impossible. When the alphabet has
three or more letters, one will most probably create a word in which the
addition of any letter invariably creates a square. When one restricts the set
of undesired squares to a finite one, this can be possible. We study the
constraints on the alphabet and the set of squares which permit this approach
to work.Comment: 18 page
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