The first few most recent pending maps:

Identifier
Mp00000: Graphs block-cut treeGraphs
Description
Sends a graph to its block-cut tree.
The block-cut tree has a vertex for each block and for each cut-vertex of the given graph, and there is an edge for each pair of block and cut-vertex that belongs to that block. A block is a maximal biconnected (or 2-vertex connected) subgraph. A cut-vertex is a vertex whose removal increases the number of connected components.
References
Sage code
def mapping(G):
from sage.graphs.connectivity import blocks_and_cuts_tree
return blocks_and_cuts_tree(G)


Created
Dec 02, 2022 at 01:18 by Harry Richman
Updated
Dec 02, 2022 at 01:18 by Harry Richman
Sage cell
Please click on evaluate and search for map before submitting your map!
Identifier
Mp00000: Permutations catalanizationPermutations
Description
The catalanization of a permutation.
For a permutation $\sigma$, this is the product of the reflections corresponding to the inversions of $\sigma$ in lex-order.
A permutation is $231$-avoiding if and only if it is a fixpoint of this map. Also, for every permutation there exists an index $k$ such that the $k$-fold application of this map is $231$-avoiding.
(Please do not accept yet, I just record it here and wait for the paper to be published.)
Sage code
def mapping(pi):
Pi = Permutations(len(pi))
return prod([Pi(Permutation(t)) for t in sorted(pi.inversions())], Pi.one())

Properties