4 papers · 1 filter
Repeated Lefschetz-like decompositions for flag doubly Cohen--Macaulay simplicial complexes and gamma vectors of flag spheres
Soohyun Park
We find decompositions of -polynomials of flag doubly Cohen-Macaulay simplicial complex that yield a direct connection between gamma vectors of flag spheres and constructions us…
Recursive properties of Cohen--Macaulay flag simplicial complexes and Lefschetz decompositions from -vectors
Soohyun Park
Most applications of the hard Lefschetz theorem related to combinatorial properties of simplicial complexes involve their -vectors. In the context of positivity properties invol…
-vectors of balanced simplicial complexes, flag spheres, and geometric Lefschetz decompositions
Soohyun Park
We show that there are -vectors of balanced simplicial complexes giving a source of simplicial complexes exhibiting a Boolean decomposition similar to a geometric Lefschetz deco…
Flag complex face structures and decompositions
Soohyun Park
One of the most common and effective methods of obtaining structural information on simplicial complexes is to use tools from algebraic geometry/commutative algebra (often motivate…