**The first few most recent pending maps**:

Description

Sends a graph to its block-cut tree.

The

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!searching the database

This map was not found in the database.

Identifier

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.)

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

graded

Created

Feb 19, 2021 at 14:02 by

**Christian Stump**
Updated

Feb 19, 2021 at 14:02 by

**Christian Stump**Sage cell

Please click on

**evaluate**and**search for map**before submitting your map!searching the database

This map was not found in the database.