poseticDataAnalysis (version 1.0.0)

DisjointSumPOSet: Disjoint sum of posets.

Description

Computes the disjoint sum of the input posets.

Usage

DisjointSumPOSet(poset1, poset2, ...)

Value

The disjoint sum poset, an object of S4 class POSet.

Arguments

poset1

An object of S4 class POSet. Argument poset1 must be created by using any function contained in the package aimed at building object of S4 class POSet (e.g. POSet(), LinearPOSet(), ProductPOSet(), ...).

poset2

An object of S4 class POSet. Argument poset2 must be created by using any function contained in the package aimed at building object of S4 class POSet (e.g. POSet(), LinearPOSet(), ProductPOSet(), ...).

...

Optional additional objects of S4 class POSet. Optional arguments must be created by using any function contained in the package aimed at building object of S4 class POSet (e.g. POSet(), LinearPOSet(), ProductPOSet(), ...).

Details

Let \(P_1=(V_1,\leq_1),\ldots,P_k=(V_k,\leq_k)\) be \(k\) posets on disjoint ground sets. Their disjoint sum is the poset \(P=(V,\lhd)\) having as ground set the union of the input ground sets, with \(a\leq b\) if and only if \(a,b\in V_i\) and \(a\leq_i b\) for some \(i\).

Examples

elems1 <- c("a", "b", "c", "d")
elems2 <- c("e", "f", "g", "h")

dom1 <- matrix(c(
  "a", "b",
  "c", "b",
  "b", "d"
), ncol = 2, byrow = TRUE)

dom2 <- matrix(c(
  "e", "f",
  "g", "h",
  "h", "f"
), ncol = 2, byrow = TRUE)

pos1 <- POSet(elements = elems1, dom = dom1)

pos2 <- POSet(elements = elems2, dom = dom2)

dsj.sum <- DisjointSumPOSet(pos1, pos2)