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User:Pontus von Brömssen
I obtained my PhD in mathematics at Uppsala University in 1999.
Contents
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:
- Cellular automata on graphs:
Graph theory
Special graphs and invariants
Enumeration of substructures (and extremal sizes of those)
Graphs | Number | Hamiltonian (or longest) | Most common length |
---|---|---|---|
Kneser graph | A354568 | ||
2-Fibonacci digraph | A359997, A360000 |
A359998 | A359999 |
Euclid’s orchard graph | A360063 |
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 |
Graphs | Independence no | Maximum | Maximal |
---|---|---|---|
de Bruijn graph | A006946 | A333078 | A333077 |
2-Fibonacci digraph | A359994 | A359996 | A359995 |
Graphs | Spanning trees | Graceful labelings | Connected spanning subgraphs |
---|---|---|---|
Hypercube | A006237 | A338005 | A372705 (See also A373034, A373035.) |
Fibonacci cube | A336832 | ||
Grid graph | A007341, A116469 | A336833 | A359992, A359993 (See also A373036, A373037.) |
Grid graph in arbitrary dimension | A338832 | ||
Euclid’s orchard graph | A360062 |
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 | ||
-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
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 |
-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 |
Tournaments
- Variance of subgraph counts in random tournaments: A373775, A373776, A373777.
- Tournaments with the largest possible automorphism group: A374164.
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 (A007318) | A364152 (first term for each n) |
n-gonal numbers (A057145) | A374370 (array), A374371 (first term for each n) |
Pentagonal numbers (A000326) | A374372 |
Hexagonal numbers (A000384) | A374373 |
Oblong numbers (A002378) | A374374 |
Numbers of the form k*(k+1)*(k+2) (A007531) | A374375 |
n-gonal pyramidal numbers (A080851) | A374498 (array), A374499 (first term for each n) |
Square pyramidal numbers (A000330) | A374500 |
Pentagonal pyramidal numbers (A002411) | A374501 |
Hexagonal pyramidal numbers (A002412) | A374502 |
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 |
One can also define a bipartite graph with a vertex for each (n-1)-celled polyomino in the first part, a vertex for each n-celled polyomino in the second part, and an edge between two polyominoes if one of them can be obtained from the other by adjoining one cell. A367441 gives the number of polyominoes in the first part needed to cover the second part. A367443 gives the degrees of the polyominoes in the first part. Also related are A373635 (number of n-celled polyominoes for which two inequivalent cells can be adjoined such that the two resulting (n+1)-celled polyominoes are identical), A373636 (ditto for polyhexes), and A373637 (polyiamonds).
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
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 |
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 |