A long-standing conjecture of Stanley states that every Cohen–Macaulay simplicial complex
is partition-able. We disprove the conjecture by constructing an explicit counterexample …

Let $ G $ be a graph with $ n $ vertices and $ S=\mathbb {K}[x_1,\dots, x_n] $ be the
polynomial ring in $ n $ variables over a field $\mathbb {K} $. Assume that $ J (G) $ is the …

Much information about a graph can be obtained by studying its spanning trees. On the
other hand, a graph can be regarded as a 1-dimensional cell complex, raising the question …

We use the notion of Borel generators to give alternative methods for computing standard
invariants, such as associated primes, Hilbert series, and Betti numbers, of Borel ideals …

Let $\mathbb {K} $ be a field and $ S=\mathbb {K}[x_1,\dots, x_n] $ be the polynomial ring in
$ n $ variables over the field $\mathbb {K} $. Let $ G $ be a forest with $ p $ connected …

We investigate the rational powers of ideals. We find that in the case of monomial ideals, the
canonical indexing leads to a characterization of the rational powers yielding that symbolic …

Let G be a graph with n vertices and let S= K [x 1,…, xn] be the polynomial ring in n variables
over a field K. Assume that J (G) is the cover ideal of G and J (G)(k) is its k-th symbolic …

In this paper we study depth and Stanley depth of the quotient rings of the edge ideals
associated with the corona product of some classes of graphs with arbitrary non-trivial …

arXiv:1409.6072v1 [math.AC] 22 Sep 2014 Page 1 arXiv:1409.6072v1 [math.AC] 22 Sep
2014 Stanley depth of powers of the path ideal Alin Stefan Petroleum and Gas University of …

Over the last 25 years the study of algebraic, homological and combinatorial properties of
powers of ideals has been one of the major topics in Commutative Algebra. In this article, we …