User:Pontus von Brömssen

I obtained my PhD in mathematics at Uppsala University in 1999.

A selection of sequences I contributed to the OEIS

Sequences authored or coauthored by me are shown in bold. Some other sequences are included to make certain sets of related sequences complete.

Cellular automata

Maximum periods

• Cyclic elementary cellular automata:
  • Sizes for which the maximum period, starting with a single cell, is not divisible by the size: A357867.
  • Maximum period with any initial configuration: A357950.
• Cellular automata on graphs:
  • Outer totalistic: A357951.
  • Totalistic: A357952, A357953.

Graph theory

Special graphs and invariants

Enumeration of substructures (and extremal sizes of those)

Cycles

Graphs	Number	Hamiltonian (or longest)	Most common length
Kneser graph		A354568
2-Fibonacci digraph	A359997, A360000	A359998	A359999
Euclid’s orchard graph		A360063

Maximum length of induced paths and cycles

Graphs	Paths	Cycles
Square grid	A331968	A357357
Square torus	A357359	A357358
Hypercube	A099155, A357360, A357499	A000937
Knight graph	A357500
King graph		A357501
Fibonacci cube	A357619	A357620
Halved cube	A358355	A358356
Folded cube	A358357	A358358

Independent sets

Graphs	Independence no	Maximum	Maximal
de Bruijn graph	A006946	A333078	A333077
2-Fibonacci digraph	A359994	A359996	A359995

Other substructures

Graphs	Spanning trees	Graceful labelings
Fibonacci cube		A336832
Grid graph		A336833
Grid graph in arbitrary dimension	A338832
Euclid’s orchard graph	A360062

Subgraphs of hypercube graphs

Symmetries	All subgraphs	Connected subgraphs
None	A001146	A290758, A369999
Automorphisms of the hypercube (exact copies)	A000616, A039754	A369606, A369605
Isomorphism	A369996, A369995	A369998, A369997

Other graph invariants

• Intersection number of Turán graphs: A355756.
• Number of automorphisms of the folded cube graph: A357827.

Enumeration of graphs by number of vertices and a given invariant or property

Property or invariant	Unlabeled		Labeled
	All	Connected	All	Connected
Even	A000568	A334335
Lights out unique	A334444	A334443
$C_{4}$-free	A352068	A079566
Weakly pancyclic		A363362, A363363
1-tough	A366755
Minimally 1-tough	A366756
Zero forcing number		A343648
Throttling number		A343649
Metric dimension		A348600
Stepping stone number		A350785
Degeneracy		A352067
Bipartite dimension	A355334	A355335	A355333
Intersection number	A355754	A355755
Packing chromatic number	A363043	A363044
Clique XOR sum reachability	A370072	A370073	A370609

Haar graphs

A357000, A357001, A357002, A357003, A357004, A357005, A357006.

Line intersection graphs

A371437, A371438, A371439.

Extremal graph theory

Largest number of maximal induced subgraphs with a given property

Property	Sequence
Empty/complete	A000792
Acyclic	A342211
Bipartite	A342212
Planar	A342213
Chordal	A342324
3-colorable	A352208
Perfect	A352209
2-degenerate	A352210
Cluster graph	A352211
Triangle free	A352212
Cograph	A352213
Claw-free	A352214
$C_{4}$-free	A352215
Diamond-free	A352216

Inducibility (maximum number of induced copies of a given graph or family of graphs)

Graph	Sequence
4-vertex path	A352665
Claw graph	A352666
Paw graph	A352667
Diamond graph	A352668
Cycles	A352669

Universal graphs

Graphs	Sequence(s)
All	A097911
Connected	A370003
Cycles	A370301, A370302, A370303
Trees	A348638

Other

• Least number of edges of an asymmetric graph: A352764, A352765.
• Largest number of orientations: A352766, A352767.
• Largest bipartite dimension: A355336.
• Least number of edges that guarantees weak pancyclicity in non-bipartite graphs: A363364.
• Maximum number of induced subgraphs (up to isomorphism): A370001, A370002 (connected subgraphs).

Graphs of graphs

Vertices correspond to all graphs in a given class, adjacency is given by a certain condition.

		Unlabeled		Labeled
Adjacency condition	Invariant	All	Connected	All	Connected
Complementation of an induced subgraph	Coordination sequence	A370072	A370073	A370609

Other

• Number of vertices of the perfect fractional matching polytope of complete graphs: A269799.
• Number of unlabeled hypergraphs by number of vertices and edges: A371830.

Number theory

Base dependent sequences

Digit deletion

• Periods for Fibonacci recurrence: A306773.
• Periods for multiplication by 2: A335502.
• Periods for multiplication by 3: A335503.
• Periods for multiplication by 4: A335504.
• Periods for multiplication by 5: A335505.
• Multiplication by 5, delete digit 7: A335506.

Other

• Number of digits in base -2: A027615.
• Doubling in base n by moving the last digit to the front: A087502.
• Digital derivative: A333979.
• Smallest power of 2n+1 with equal number of binary 0’s and 1’s: A364608.
• Powers of 2 whose average digit is closer to 9/2 than for any smaller power of 2: A364615.
• Powers of 3 with a specified number of binary 1’s: A364650, A365214, A365215.
• Numbers with expected average of digits in bases 2..n: A364714.

Numbers that can be written as products of numbers in the same sequence

Base sequence	Sequence of products (or indices of products)
Partition numbers (A000041)	A363492
Lucky numbers (A000959)	A363634
Ludic numbers (A003309)	A363635
Squares plus 1 (A002522)	A363636
Squares less 1 (A005563)	A363637
Primes plus 1 (A008864)	A363638
Primes less 1 (A006093)	A363750
Tetrahedral numbers (A000292)	A364151
n-simplex numbers	A364152 (first term for each n)

Polyforms

Lists of polyforms by code

Polyform	Free	Fixed
Polyominoes	A246521
Polyplets	A364927
Corner-connected polyominoes	A364928
Polycubes	A365139
4-dim. polyhypercubes	A365140
5-dim. polyhypercubes	A365141
Polyhypercubes in arbitrary dim.	A365142

A365143 gives the proper dimensions of the polyhypercubes in A365142.

Properties of polyomino graphs

For a given n, define a graph with one vertex for each (free) n-celled polyomino and an edge between two polyominoes if one can be obtained from the other by moving a single cell. There are two versions depending on whether the intermediate (the set of cells remaining when the cell to be moved has been detached) is required to be a connected polyomino or not.

Invariant	Connected intermediate	Intermediate not required to be connected
Number of edges	A367435	A098891
Vertex degrees	A367439	A367126
Maximum degree	A367437	A367124
Number of vertices with max degree	A367438	A367125
Number of Hamiltonian cycles	A367436	A367123
Independence number	A367440	A367127
Domination number		A365621

See also A367441, A367443.

Rooted (or pointed) polyforms

Polyform	Enumeration	Least no from a polyform	Number of extremal
Polyominoes	A126202	A367758	A367759
Polyhexes	A369362	A369363	A369364
Polyiamonds	A369365	A369366	A369367

Occurrence in random growth models

Free polyominoes

Growth model	Individual probabilities	Greatest probability	Least probability
Eden growth model	A367760, A367761	A367762, A367763
Eden growth model (version 2)	A367671, A367672	A367673, A367674
Random walk	A367994, A367995	A367998, A367999	A367996, A367997
Internal diffusion-limited aggregation	A368386, A368387	A368390, A368391	A368388, A368389
External diffusion-limited aggregation	A368660, A368663, A368664, A368665, A368666, A368667, A368668, A368669	A368662	A368661

Fixed polyominoes

Growth model	Individual probabilities	Greatest probability	Least probability
Eden growth model	A367764, A367765	A367766, A367767
Eden growth model (version 2)	A367675, A367676	A367677, A367678
Random walk	A368000, A368001	A368004, A368005	A368002, A368003
Internal diffusion-limited aggregation	A368392, A368393	A368394, A368395
External diffusion-limited aggregation	A368863	A368865	A368864