============  KNIGHT's TOUR NOTES   by G. P. Jelliss , 2019 =============
direct links for downloading the volumes as .pdf - files :  http://www.mayhematics.com/p/p.htm


The Volumes in the Series
1. Theory of Moves 
(Including theory of symmetry and magic and knight-move geometry)
2. Walker Tours 
(About lateral and diagonal movers Wazir, Rook, King, Queen )
3. Shaped & Holey Boards 
(A collection of knight tours exploring varieties of symmetry)
4. Oblong Boards 
(Including history of 4×8 knight tours and new results on magic rectangles)
5. Odd and Oddly Even Boards 
(With large sections on 6×6 and 10×10 knight tours)
6. Geometry of Chessboard Knight Tours 
(History of 8×8 tours, with study of crosspatch patterns and enumeration).
7. Symmetry in Chessboard Knight Tours 
(Approximate, exact and mixed symmetry, on evenly even  boards)
8. Octonary & Quaternary Pseudotours 
(Catalogued with some tours derived from them)
9. Magic Knight Tours 
(With a complete catalogue of 8×8 and examples on larger boards)
10. Augmented Knight & Leaper Tours 
(Tours by compound movers and longer leapers).
11. Alternative Worlds 
(Figured, Lettered Tours, Bent Boards, Space Chess,  Honeycombs)
12. Chronology & Bibliography of Tours 
(With acknowledgmants and outline of the series)

===================== contents ========================

volume 1 , Theory of Moves
Movement
3. Boards, Moves and Pieces
6. Freedom and Multiplicity, Mobility
8. Journeys, Journey Equations, Reduced, Compact
11. Shortest Path Problem, Shortest Knight Paths, Houston's Problem 
14. Two-move Paths, Angles, 16 Four and Six=move Circuits
17. Eight-move Symmetric Circuits, 
19. Touring Tests
Symmetry 
20. What are We Counting? Terminology. 22 Aesthetics of Symmetry.
23. Symmetry in Open and Closed Paths
25. Symmetry in Rectangular Knight Tours 
26. Symmetry in Square Knight Tours, Piecewise Symmetry.
Magic
27. Magic Arrays. 28. Magic Rectangles. 
29. Some History of Magic Squares 3×3, 4×4.
30. The Step-Sidestep Method.
31. Natural Magic
33. Magic Tours, Magic Rectangle Tours
35. Existence Theorems for Magic Leaper Tours. 
37. Which Boards Have Magic Tours?
Knight-Move Geometry
38. Nets, Planarity
40. Straits and Slants, Eccentrics 
42. Pseudotours, Borders, Simple Linking
45. Cell Coding, Generic Moves, Central Angles
49. Intersections, Triangles, Quadrilaterals, Polygons.
Smallest Knight-Tourable Boards 
53. 7 to 9-cell boards.
56. 10 and 11 cell boards.
58. 12-cell boards
End Pages
66. Glossary
72. Puzzle Solutions
73. 


volume 2 , Walker Tours
Lateral Movers
3. Labyrinths
5. Wazir Tours 2×n  3×n, 
8. 4×n, 5×n  
12. 6×6  8×8 
14. 10×10 & larger 
16. Non-crossing Rook Tours 
17. Figured Wazir Tours 
18. Rook around the Rocks 
20. Rook Tours, One-Rank, Two-Move Rook
22. Three-Move Rook, Hyperwazir 
23. Four-Move Rook, More-Move Rooks. 
Diagonal Movers 
25. Knots 
27. King Tours: 2×n, 3×n 4×n 5×n 6×n 7×n 
36. 8×8 King Tours, Alternating, Figured, Magic 
39. 8×8 King Tours, Diagonally Magic Biaxial
42. 8×8 King Tours, Diagonally Magic Axial, and 16×16 Example 
44. Queen Tours: Two-Move Queens
46. Three-Move Queens, Pterodactyl 
48. Four-Move Queens, More-Move Queens.
Rider and Hopper Tours
53. Rook Crossover, Bishop Crossover.
54. Queen Crossover, Bouncer
55. Grasshopper
56. Moose and Nightriderhopper
Postscript
57. Puzzle Solution


volume 3 , Shaped & Holey Boards
Octonary
3. Number of cells 8 to 80 in steps of 8 
Birotary
7. Number of cells 16 to 196 in steps of 4
Biaxial
24. Number of cells 10 to 52 in steps of 2
Rotary (Eulerian and Bergholtian)
32. Number of cells 13 to 248
Axial (Sulian and Murraian)
53. Number of cells 14 to 124
Unary (Asymmetric)
64. Number of cells 13 to 160
79. 


volume 4 , Oblong Boards
Oblong Boards
3. Which Oblong Boards Have Tours?
Three-Rank Boards  
4. General Principles
5. Centre File Formations
7. Repeating Patterns. Catalogue 3×4 to 3×7
9. 3×8 
12. 3×9
17. 3×10 
18. 3×11
20. 3×12
21. 3×13
22. 3×14
24. 3×15, 3×16
25. 3×17 to 3×20
Four-Rank Boards 
26. Saint-Marie's Theorem. 
27. Recurrences for Counting Half-Tours. 4×3
28. 4×4. Edge-Hugging Tours. 4×5
29. 4×6 
32. 4×7 
34. History of 4×8 Tours.
44. 4×9, 4×10
45. 4×11, 4×12
48. 4×13, 4×14, 4×15, 4×16
49. 4×17, 4×18
50. 4×19, 4×20
51. 4×22, 4×24, 4×26,  4×28 (all magic)
Five-Rank Boards 
52. 5×6 to 5×20
Six-Rank Boards 
56. 6×7 to 6×12 (magic)
Seven-Rank Boards 
60. 7×8 to 7×17
Eight-Rank Boards
62. 8×9 to 8×25
Larger Oblongs 
65. 9×10, 9×11, 10×11, 
66. 10×12 (magic) 11×13, 12×14 (magic), 17×19, Puzzle Solution 
67. 20×32, 24×37


volume 5 , Odd & Oddly Even Boards
Odd Square Boards 
3. The 5×5 Board
7. The 7×7 Board
9. The 9×9 Board
10. The 11×11 Board
11. The 13×13 Board. The 15×15 Board
Oddly Even Square Boards 
12. The 6×6 Board. Quaternary Symmetry.
14. Binary Symmetry
15. Central Angle Method
16. Straits and Slants
17. Open Tours with Three Slants
18. Catalogue of 6×6 Asymmetric Closed Tours
19. Four Slants
31. Eight Slants
47. Ten Slants
57. Twelve Slants
58. Semimagic Tours
59. Figured Tours
60. The 10×10 Board. Asymmetric Tours
61. Binary 
62. Quaternary
65. My Own Work 
66. No Right Angles 
67. Celtic, Bordered, Pseudotours
68. Semimagic, Figured
69. The 14×14 Board
71. The 18×18 Board
73. Larger Oddly-Even Boards (30×30).


volume 6 ,  Geometry of Chessboard Knight Tours
Some History of Knight Tours
3. The Earliest Full-Board Tours
5. Rediscovery of the Problem 1725-1823
16. Squares and Diamonds 1823-1847
Rogetian Tours
21. Roget's Nets 1840 
22. Enumeration of Rogetian Open Tours
24. Enumeration of Rogetian Closed Tours (and of Squares and Diamonds Type).
Angles in 8×8 Knight Tours
25. Tours with All Six Angles. Minimum Angle Tasks.
27. Double Minima Tasks
29. Maximum Angle Tasks.
32. Circulation.
33. Directions: Modes and Senses
Shapes in 8×8 Knight Tours
35. Triangles
36. Quadrilaterals, Squares, Oblngs, Lozenges, Diamonds
38. Intersections, Uncrossed Moves, Slants, Eccentrics
41. Stars
Graphic Tours
43. Pictorial
44. Monogram
Crosspatch Pseudotours & Compartmental Tours
48. Crosspatch Patterns
49. Tours from the Strait Crosspatches
51. Tours from the Slant Crosspatches
Some More Enumerations
55. Double Halfboard Tours
57. Collinian Tours
61. Enumeration of Double-Halfboard Rhombic Tours.
67. Enumeration of Full-Board Rhombic Tours.
79. Enumeration of All 8×8 Knight Tours  


volume 7 , Symmetry in Chessboard Knight Tours 
Asymmetry
3. Synthetic Tours
5. Irregularity
Approximate Symmetry
7. Octonary, Biaxial 
10. Axial 
14. Birotary 
15. Bergholtian 
16. Diagonal 
Exact Symmetry 
17. Historical Examples
25. Symmetrisation 
27. Constructing Symmetric Tours
29. Converting Pseudotours to Tours
30. A Complete Central Angle Collection 
Mixed Quaternary Symmetry
41. General Principles
42. Mixed Symmetry on the 8×8 Board. Tours with h = 1.
43. The 16 tours of type (1:10:5)
44. The 16 tours of type (1:8:7)
45. The 16 tours of type (1:6:9)
46. Mixed Quaternary Tours with k = 3 
46. Triple move (1·8 + 2·4)
47. Double move (1·8 + 3·4)
49. Double move (2·8 + 1·4)
53. Single moves (3·8)
55. Single moves (2·8 + 2·4)
64. Mixed Quaternary Tours with h > 1 and k > 3 (h=3, j=4, k=5)
68. Summary of the Catalogue. Maximum Octonary Symmetry.
69. Mixed Quaternary Symmetry on the 12×12 Board.
Other Evenly Even Tours
74. Some 12×12 Tours
77. Some 16×16 Tours


volume 8 , Octonary & Quaternary Pseudotours 
Octonary Pseudotours
3. Catalogue
5. Tours Derived from Octonary Pseudotours
Quaternary Pseudotours
8. Method of Classification
9. Catalogue 8-fold
10. Catalogue 4-fold
22. Catalogue 2-fold
47. Catalogue 1-fold
62. Table & Other Quaternary Pseudotours
Tours Derived from Quaternary Pseudotours
66. Vandermondian Tours
67. Jaenischian Tours
68. Aladdin's Conundrum
68. Linking Non-Crossing Circuits
Larger Pseudotours
70. Board 16×16 
71 Board 32×32 Board


volume 9 , Magic Knight Tours
Construction Methods
3. Method of Quartes. Regular Quartes.
6. Irregular Quartes. Classification of Regular Magic Tours
7. Contraparallel Chains, The X&N Notation, 
9. Murray's Testings Procedure
10. The Method of Braids
History of  8×8  Magic Knight Tours
11. First Magic Knight Tours (1848-1876)
Beverley, Wenzelides, Mysore, Jaenisch
17. The Age of Magic Tours (1876-1886)
Feisthamel Bouvier Caldwell Exner Reuss Francony Beligne Ligondes
29. Taking Stock (1886-1986)
Parmentier, Falkener, Grossetaite, Ligondes, Lehmann, Murray
34. Completing the Task (1986-2003)
Jelliss, Marlow, Roberts, Mackay, Meyrignac & Stertenbrink
Catalogue of 8×8 Magic Knight Tours 
38.. Historical
41. Geometric Catalogue 
48. Arithmetic Catalogue
Magic Knight Tours on Larger Boards
63 12×12
68 16×16
74 20×20
75 24×24
77 32×32 
80  48×48


volume 10 , Augmented Knight & Leaper Tours
Augmented Knights 
3. Two-Move Knighted Pieces, Emperor
8. Templar, Empress, 
11. Prince, 
12. Hospitaller, Night-Commuter, Lancelot
13. Nightrider
14. Three-Move Knights
23. Four-Move Knights 
25. Five-Move and Six-Move Knights 
26. Seven-Moves Knights.
The Big Beasts 
27. Camel {1,3} Shaped boards, 
31. Zebra {2,3} 
33. Giraffe {1,4} 
36. Antelope {3,4} 
37. {1,5} {2,5} 
38. {3,5} {1,6} {1,7} {4,7} {6,7}  
Augmented Beasts
39. Two-Move Beasts  
40. Gnu 
41 Okapi, Bison, Zebrarider 
43 Fiveleaper 
49 Root-50, 
50. Root-65, 
51. Root-85 
51. Three-Move Beasts, 
55. Four-Move-Beasts,
62. Five-Move Beasts 
66. Six-Move Beasts
74. Seven-Move Beasts
77. Eight-Move Beasts
79. More-Move Beasts
80. Wizard, Puzzle Solution.


volume 11 , Alternative Worlds
Lettered Tours
3. Verse Tours
4. Coordinates, Acrostics
5. Alphabetical Numbering
6. Cryptotours
13. Crossword Puzzle Tours
Non-Crossing Tours
14. Historical Introduction
15. Methods of Construction, Some Analysis
16. Knight Open Path Solutions
21. Knight Closed Path Solutions
25. Knight Solutions with Quaternary Symmetry
27. Non-Crossing Leaper Tours, Gnu, Camel, Zebra, Giraffe, Antelope.
Figured Tours
30. Two Mediaeval Puzzles. History of Figured Tours
32. Dawsonian Figured Tours 33. Axial 37. Rotary
38. Other Dawsonian Tours. 41 Squares in other Formations.
42. Other Numbers in Figured Tours. 43. My Own Work on Figured Tours.
46. Figured Tours 12×12 and 47. Figured Tour 16×16. 
Alternative Boards
48. Bent Boards
51. Space Chess
60. Honeycomb Boards
Puzzle Solutions
65-66. Cryptotours Decyphered


volume 12 , Chronology & Bibliography of Tours
Chronology
3. to 1759
4. to 1824
5. to 1847
6. to 1861
7. to 1873
8. to 1884
9. to 1900
10. to  1917
11. to 1929
12. to 1935
13. to 1944
14. to 1959
15. to 1978
16. to 1985
17. to 1994
18. to 2000
19. to 2008
20. to 2019
Bibliography
21. A
23. B
29. C
32. D
35. E
36. F
39. G
41. H
44. I J
49. K
51. L
55 M
61. N
62. O P
64. Q R
66. S
70. T
71. U V
73. W
76. X Y Z
Knight's Tour Notes
77. Acknowledgments and Outline 
78. The Volumes in the Series