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Enumeration:

A338562 — Number of cyclic diagonal Latin squares of order N

A123565 — Number of cyclic diagonal Latin squares of order N with fixed first row (was known before me, interconnection with cyclic DLSs established)

A232991 (for n), A011655 (for 2n+1) — Binary sequences for cyclic diagonal Latin squares (was known before me, interconnection with existense of cyclic DLS of corresponding orders established)

A341585 — Number of main classes of diagonal Latin squares of order N that contain cyclic DLS (N<23), proving list

A343866 — Number of inequivalent cyclic diagonal Latin squares of order 2n+1 up to rotations, reflections and permutation of symbols (calculated by A. Howroyd)

Transversals:

A348212 — Number of transversals in cyclic diagonal Latin squares of order N (N<26)

A342998 — Minimum number of diagonal transversals in a cyclic diagonal Latin square of order N=2n+1 (N<20), proving list

A342997 — Maximum number of diagonal transversals in a cyclic diagonal Latin square of order N=2n+1 (N<20), proving list

Intercalates:

Number of intercalates is zero for all cyclic DLS

Main classes:

Axxxxxx — Minimum cardinality of main class for cyclic diagonal Latin squares of order N=2n+1 (N<16)

Axxxxxx — Maximum cardinality of main class for cyclic diagonal Latin squares of order N=2n+1 (N<16)

Numerical spectra:

A120325 — Transversals in cyclic diagonal Latin squares of order N=2n+1 (values of transversals number are same for all cyclic DLS of selected order N, so cardinality of spectrum is equal to 1 if cyclic DLS are exist for order N, and equal to 0 otherwise)

A341585 — Diagonal transversals in cyclic diagonal Latin squares of order N=2n+1 (same as main classes number at least for orders N<=19), proving lists (1, 5, 7, 11, 13, 17, 19)

A------ — Intercalates in cyclic diagonal Latin squares of order N (all are equal to 0)

Orders for which cyclic DLS are exist:

A007310 — List of orders

A120325 — Binary series (with displacement +3)

Enumeration:

A342990 — Number of horizontally semicyclic diagonal Latin squares of order N=2n+1 (N<34)

A071607 — Number of horizontally semicyclic diagonal Latin squares of order N=2n+1 with constant first row (N<20) (was known before me, interconnection with semicyclic DLSs established)

A366331 — Number of main classes of diagonal Latin squares of order N=2n+1 that contain horizontally semicyclic DLS (N<23), proving lists (33 KB)

Transversals:

A348212 — Number of transversals in semicyclic DLS of order N=2n+1 (equal to number of transversals in cyclic LS/DLS of order N=2n+1)

A366332 — Minimum number of diagonal transversals in semicyclic DLS of order N=2n+1 (N<23), proving list

A342997 — Maximum number of diagonal transversals in semicyclic DLS of order N=2n+1 (equal to maximum number of diagonal transversals in cyclic DLS of order N=2n+1)

Intercalates:

A------ — Intercalates in semicyclic DLS of order N (all of them are zero)

Numerical spectra:

A120325 — Transversals in semicyclic DLS of order N=2n+1 (number of transversals is same for all semicyclic DLS, so cardinality is equal to 1 if cyclic DLS exists for selected order N, and equal to 0 otherwise)

A366333 — Diagonal transversals in semicyclic DLS of order N=2n+1 (N<23), proving lists (1, 5, 7, 11, 13, 17, 19), graphical view

A------ — Intercalates in semicyclic DLS of order N (all are zero)

Orders for which semicyclic DLS are exist:

A007310 — List of orders

A120325 — Binary series (with displacement +3)

Enumeration:

A368027 — Number of Dabbaghian-Wu pandiagonal LS of order N=2n+1

A369379 — Number of Dabbaghian-Wu pandiagonal LS of order N=2n+1 with fixed first row

A369380 — Number of main classes of DLS that contain Dabbaghian-Wu pandiagonal LS of order N=2n+1

Enumeration:

Axxxxxx — Number of Atkin-Hey-Larson semicyclic pandiagonal LS of order N=2n+1 without 45k degree rotations, with constant first row (N<16)

A343867 — Number of Atkin-Hey-Larson semicyclic pandiagonal LS of order N=2n+1 with constant first row (N<32) (was known before, verified for N=13)

Enumeration:

Axxxxxx — Number of rotated semicyclic DLS of order N=2n+1 (N<23)

Axxxxxx — Number of rotated semicyclic DLS of order N=2n+1 with fixed first row (N<23)

Axxxxxx — Number of main classes of DLS of order N=2n+1 that contain rotated semicyclic DLS (N<23), proving lists

Transversals:

Axxxxxx — Minimum number of transversals in rotated semicyclic DLS of order N=2n+1 (N<23), proving list

A348212 — Maximum number of transversals in rotated semicyclic DLS of order N=2n+1 (equal to number of transversals in cyclic LS/DLS of order N)

Axxxxxx — Minimum number of diagonal transversals in rotated semicyclic DLS of order N=2n+1 (N<23), proving list

A342997 — Maximan number of diagonal transversals in rotated semicyclic DLS of order N=2n+1 (equal to maximum number of diagonal transversals in cyclic DLS of order N)

Intercalates:

A------ — Minimum number of intercalates in rotated semicyclic DLS of order N (all are zero)

Axxxxxx — Maximum number of intercalates in rotated semicyclic DLS of order N=2n+1 (N<23), proving list

Numerical spectra:

Axxxxxx — Transversals in rotated semicyclic DLS of order N=2n+1 (N<23), proving lists (1, 5, 7, 11, 13, 17, 19)

Axxxxxx — Diagonal transversals in rotated semicyclic DLS of order N=2n+1 (N<23), proving lists (1, 5, 7, 11, 13, 17, 19), graphical view

Axxxxxx — Intercalates in rotated semicyclic DLS of order N=2n+1 (N<23), proving lists (1, 5, 7, 11, 13, 17, 19)

Orders for which rotated cyclic DLS are exist:

A007310 — List of orders

A120325 — Binary series (with displacement +3)

Enumeration:

A372922 — Number of diagonalized cyclic DLS of order N=2n+1 (N<14)

A372923 — Number of diagonalized cyclic DLS of N=2n+1 with fixed first row (N<14)

Axxxxxx — Number of main classes of diagonalized semicyclic DLS of N=2n+1 (N<14), proving list

Transversals:

A348212 — Number of transversals in diagonalized cyclic DLS of order N=2n+1 (equal to number of transversals in cyclic LS/DLS od order N=2n+1)

Axxxxxx — Minimum number of diagonal transversals in diagonalized cyclic DLS of order N=2n+1 (N<14), proving list

Axxxxxx — Maximum number of diagonal transversals in diagonalized cyclic DLS of order N=2n+1 (N<14), proving list

Intercalates:

Number of intercalates in all diagonalized cyclic DLS is equal to zero

Numerical spectra:

A120325 — Transversals in diagonalized cyclic DLS of order N=2n+1 (values of transversals number are same for all diagonalized cyclic DLS of selected order N, so cardinality of spectrum is equal to 1 if cyclic DLS are exist for order N, and equal to 0 otherwise)

Axxxxxx — Diagonal transversals in diagonalized cyclic DLS of order N=2n+1 (N<14), proving lists (1, 5, 7, 9, 11, 13), graphical view (5, 7, 9, 11, 13, все)

A------ — Intercalates in diagonalized cyclic DLS of order N=2n+1 (all are zero)

Orders for which diagonalized cyclic DLS are exist:

all odd orders except N=3 (1, 0, 1, 1, 1, 1, 1, ...), (1, 5, 7, 9, 11, 13, ...)

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Last updated: May 16 2024