bratteliDimensions {bratteli}

Bratteli dimensions

Description

Dimensions of the vertices of a Bratteli graph.

Usage

bratteliDimensions(Mn, N)

Arguments

Mn

a function returning for each integer n the incidence matrix between levels n and n+1; the matrix Mn(0) must have one and only one row

N

the level up to which the dimensions are wanted

Value

The dimensions of the vertices in a list.

Examples

# the Pascal graph ####
Pascal <- function(n) {
 M <- matrix(0, nrow = n+1, ncol = n+2)
 for(i in 1:(n+1)) {
   M[i, ][c(i, i+1L)] <- 1
 }
 M
}
bratteliDimensions(Pascal, 4)

# the Euler graph ####
Euler <- function(n) {
  M <- matrix(0, nrow = n+1, ncol = n+2)
  for(i in 1:(n+1)) {
    M[i, ][c(i, i+1L)] <- c(i, n+2-i)
  }
  M
}
bratteliDimensions(Euler, 4)