Related papers: Constructions of Macaulay Posets and Macaulay Ring…
Poset-theoretic generalizations of set-theoretic committee constructions are presented. The structure of the corresponding subposets is described. Sequences of irreducible fractions associated to the principal order ideals of finite bounded…
It is shown that the coset lattice of a finite group has shellable order complex if and only if the group is complemented. Furthermore, the coset lattice is shown to have a Cohen-Macaulay order complex in exactly the same conditions. The…
We study three different poset structures on the set of all compositions. In the first case, the covering relation consists of inserting a part of size one to the left or to the right, or increasing the size of some part by one. The…
We introduce a new type of operad-like structure called a P-operad, which depends on the choice of some collection of posets P, and which is governed by chains in posets of P. We introduce several examples of such structures which are…
Sectional pseudocomplementation (sp-complementation) on a poset is a partial operation $*$ which associates with every pair $(x,y)$ of elements, where $x \ge y$, the pseudocomplement $x*y$ of $x$ in the upper section $[y)$. Any total…
In [1] we introduced the notion of 'structured space', i.e. a space which locally resembles various algebraic structures. In [2] and [3] we studied some cohomology theories related to these space. In this paper we continue in this…
We introduce and study a new partial order on Dyck paths. We prove that these posets are meet-semilattices. We show that their numbers of intervals are the same as the number of bicubic planar maps. We describe an unexpected connection with…
Recently it has been shown that all non-trivial closed permutation groups containing the automorphism group of the random poset are generated by two types of permutations: the first type are permutations turning the order upside down, and…
A chain poset, by definition, consists of chains of ordered elements in a poset. We study the chain posets associated to two posets: the Boolean algebra and the poset of isotropic flags. We prove that, in both cases, the chain posets…
We define piecewise-linear and birational analogues of the toggle-involutions on order ideals of posets studied by Striker and Williams and use them to define corresponding analogues of rowmotion and promotion that share many of the…
A finitely generated module $M$ over a commutative Noetherian ring $R$ is called an $I$-Cohen Macaulay module, if \[ \grade(I,M) + \dim(M/IM)= \dim(M), \] where $I$ is a proper ideal of $R$. The aim of this paper is to study the structure…
The study of topological information of spatial objects has for a long time been a focus of research in disciplines like computational geometry, spatial reasoning, cognitive science, and robotics. While the majority of these researches…
Paraorthomodular posets are bounded partially ordered set with an antitone involution induced by quantum structures arising from the logico-algebraic approach to quantum mechanics. The aim of the present work is starting a systematic…
We present a matrix-theoretic approach for studying and enumerating finite posets through their incidence representations, referred to as poset matrices. Naturally labelled posets are encoded as Boolean lower triangular matrices, allowing a…
We consider partially ordered sets of combinatorial structures under consecutive orders, meaning that two structures are related when one embeds in the other such that `consecutive' elements remain consecutive in the image. Given such a…
In this paper we describe a novel a procedure to build a linear order from an arbitrary poset which (i) preserves the original ordering and (ii) allows to extend monotonic and antitonic mappings defined over the original poset to monotonic…
The rowmotion action on order ideals or on antichains of a finite partially ordered set has been studied (under a variety of names) by many authors. Depending on the poset, one finds unexpectedly interesting orbit structures, instances of…
We investigate a certain class of posets arising from semilattice actions. Let $S$ be a semilattice with identity. Let $S$ act on a set $C$. For $c,d\in C$ put $c\leq d$ iff there is some $s\in S$ with $ds=c$. Then $(C,\leq)$ is a poset.…
A mixed lattice is a partially ordered set with two mixed partial orderings that are linked by asymmetric upper and lower envelopes. These notions generalize the join and meet operations of a lattice. In the present paper, we study…
This work introduces a notion of complexes of maximal depth, and maximal Cohen-Macaulay complexes, over a commutative noetherian local ring. The existence of such complexes is closely tied to the Hochster's ``homological conjectures", most…