We provide a combinatorial recipe for constructing all posets of height at most two which the corresponding type-A Lie poset algebra is contact. In case that such are connected, discrete Morse theory argument establishes posets' simplicial realizations contractible. It follows from cohomological result Coll and Gerstenhaber on semi-direct products contact algebras absolutely rigid.

Let G be a graph on [ n ] and J the binomial edge ideal of in polynomial ring S = K x 1 , … y . In this paper we investigate some topological properties poset associated to minimal primary decomposition We show that admits specific subposets which are contractible. This turn, provides interesting algebraic consequences. particular, characterize all graphs for depth / 4

We give a complete classification of the factorial functions of Eulerian binomial posets. The factorial function B(n) either coincides with n!, the factorial function of the infinite Boolean algebra, or 2n−1, the factorial function of the infinite butterfly poset. We also classify the factorial functions for Eulerian Sheffer posets. An Eulerian Sheffer poset with binomial factorial function B(n...

In this manuscript we study type A nilpotent Hessenberg varieties equipped with a natural S1-action using techniques introduced by Tymoczko, Harada-Tymoczko, and Bayegan-Harada, with a particular emphasis on a special class of nilpotent Springer varieties corresponding to the partition λ = (n− 2, 2) for n ≥ 4. First we define the adjacent-pair matrix corresponding to any filling of a Young diag...

Poset game, which includes some famous games. e.g., Nim and Chomp as sub-games, is an important two-player impartial combinatorial game. The rule of the game is as follows: For a given poset (partial ordered set), each player intern chooses an element and the selected element and it’s descendants (elements succeeding it) are all removed from the poset. A player who choose the last element is th...

Hierarchical data, such as Partially Ordered Set (POSET) is tremendously used in relational databases, especially in data mining and data warehouse based-applications. Unfortunately, SQL (Structured Query Language) does not effectively support hierarchical data structure to manage this sort of data, for example, in Oracle, a CONNECT BY operator is used to query data organized into trees, howeve...