Персональная страничка Ватутина Эдуарда Игоревича

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My sequences in OEIS

General type DLS

Enumeration:
  • A274171 — Number of diagonal Latin squares of order N with constant first row (N<10)
  • A274806 — Number of diagonal Latin squares of order N (N<10)
    • Transversals:
  • A287645 — Minimum number of transversals in a diagonal Latin square of order N (N<10), proving list (best known examples)
  • A287644 — Maximum number of transversals in a diagonal Latin square of order N (N<10), proving list (best known examples)
  • A287647 — Minimum number of diagonal transversals in a diagonal Latin square of order N (N<10), proving list (best known examples)
  • A287648 — Maximum number of diagonal transversals in a diagonal Latin square of order N (N<10), proving list (best known examples)
    • Main classes:
  • A287764 — Number of main classes of diagonal Latin squares of order N (N<10)
  • A299783 — Minimal size of main class for diagonal Latin squares of order N with fixed first row (N<9), proving list (best known examples)
  • A299784 — Maximal size of main class for diagonal Latin squares of order N with fixed first row (N<16), proving list (best known examples)
  • A299785 — Minimal size of main class for diagonal Latin squares of order N (N<9), proving list (best known examples)
  • A299787 — Maximal size of main class for diagonal Latin squares of order N (N<16), proving list (best known examples)
    • Intercalates, loops, Latin subrectangles and subsquares:
  • A307163 — Minimum number of intercalates in a diagonal Latin square of order N (N<25), proving list (best known examples)
  • A307164 — Maximum number of intercalates in a diagonal Latin square of order N (N<25), proving list (best known examples)
  • A307166 — Minimum number of loops in a diagonal Latin square of order N (N<8), proving list (best known examples)
  • A307167 — Maximum number of loops in a diagonal Latin square of order N (N<8), proving list (best known examples)
  • A307170 — Minimum number of partial loops in a diagonal Latin square of order N (N<8), proving list (best known examples)
  • A307171 — Maximum number of partial loops in a diagonal Latin square of order N (N<8), proving list (best known examples)
  • A307839 — Minimum number of Latin subrectangles in a diagonal Latin square of order N (N<8), proving list (best known examples)
  • A307840 — Maximum number of Latin subrectangles in a diagonal Latin square of order N (N<8), proving list (best known examples)
  • A307841 — Minimum number of nontrivial Latin subrectangles in a diagonal Latin square of order N (N<8), proving list (best known examples)
  • A307842 — Maximum number of nontrivial Latin subrectangles in a diagonal Latin square of order N (N<8), proving list (best known examples)
    • ODLS:
  • Axxxxxx — Minimum number of normalized orthogonal diagonal Latin squares for one diagonal Latin square of order N (N<13), подтверждающий список
  • A287695 — Maximum number of normalized orthogonal diagonal Latin squares for one diagonal Latin square of order N (N<10), proving list (best known examples)
    • Numerical spectra:
  • A344105 — Transversals in diagonal Latin squares of order N (N<10), proving lists (1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13), graphical view (1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, all)
  • A345370 — Diagonal transversals in diagonal Latin squares of order N (N<10), proving lists (1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13), graphical view (1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, all)
  • A345760 — Intercalates in diagonal Latin squares of order N (N<10), proving lists (1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24), graphical view (1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, all)
  • A345761 — Number of ODLS in diagonal Latin squares of order N (N<10), proving lists (1, 4, 5, 6, 7, 8, 9, 10, 11, 12), graphical view (1, 4, 5, 6, 7, 8, 9, 10, 11, 12, all)
    • Cliques from mutually orthogonal DLS:
  • A328873 — Maximal size of a set of pairwise mutually orthogonal diagonal Latin squares of order N (N<10), proving list (best known examples)
    • X-based fillings of diagonals:
  • A309283 (A338084) — Number of equivalence classes for X-based filling of diagonals in a diagonal Latin square of order n N (N<11)
  • A337302 — Number of X-based filling of diagonals in a diagonal Latin square of order N with fixed main diagonal (N<16)
  • A337303 — Number of X-based filling of diagonals in a diagonal Latin square of order N (N<16)
    • Generalized symmetries:
  • A357473 — Number of different types of generalized symmetries in DLS of order N (N<8), proving lists (4, 5, 6, 7)
  • A358515 — Number of different types of generalized symmetries in parastrofic slices in DLS of order N (N<8), proving lists (4, 5, 6, 7)

  • Axxxxxx — Minimal number of generalized symmetries in DLS of order N (N<9)
  • Axxxxxx — Miximal number of generalized symmetries in DLS of order N (N<9)
  • Axxxxxx — Spectra of number of generalized symmetries in DLS of order N (N<9)
    • Cell mapping schemes (CMS) in ODLS pairs:
  • A370389 — Number of distinct multisets of cycle lengths in the ESODLS CMS in diagonal Lain squares of order N (N<14)

    • Last updated: Dec 16 2024