Yi-Huang Shen

Tangent Cone of Numerical Semigroup Rings of Embedding Dimension Three

In this article, we give new characterizations of the Buchsbaum and Cohen–Macaulay properties of the tangent cone gr 𝔪 (R), where (R, 𝔪) is a numerical semigroup ring of embedding dimension 3. In particular, we confirm the conjectures raised by Sapko on the Buchsbaumness of gr 𝔪 (R).

On a Conjecture of Stanley Depth of Squarefree Veronese Ideals

In this article, we partially confirm a conjecture, proposed by Cimpoeaş, Keller, Shen, Streib, and Young, on the Stanley depth of squarefree Veronese ideals I n, d . This conjecture suggests that, for positive integers 1 ≤ d ≤ n, . Herzog, Vlădoiu, and Zheng established a connection between the Stanley depths of quotients of monomial ideals and interval partitions of certain associated posets. Based on this connection, Keller, Shen, Streib, and Young recently developed a useful combinatorial tool to analyze the interval partitions of the posets associated with the squarefree Veronese ideals. We modify their ideas and prove the above conjecture for . We also obtain a lower bound of sdepth(I n, d ) for any 1 ≤ d ≤ n. Our results greatly improve Theorem 1.1 in [13], and moreover, our construction leads to a direct proof of this theorem without using graph theory.

Edgewise strongly shellable clutters

When

Bounds on the Stanley depth and Stanley regularity of edge ideals of clutters

\mathcal{C}

When will the Stanley depth increase

is a chordal clutter in the sense of Woodroofe or Emtander, we show that the complement clutter is edgewise strongly shellable. When

On a class of squarefree monomial ideals of linear type

\mathcal{C}

Stanley depth of complete intersection monomial ideals and upper-discrete partitions

is indeed a finite simple graph, we study various characterizations of chordal graphs from the point of view of strong shellability. In particular, the generic graph

On the Stanley depth of squarefree Veronese ideals

G_T

LEXSEGMENT IDEALS OF HILBERT DEPTH 1

of a tree is shown to be bi-strongly shellable. We also characterize edgewise strongly shellable bipartite graphs in terms of constructions from upward sequences. \end{abstract}

Strong shellability of simplicial complexes

Let