# Boolf prop/3-ary

| # | integer partition | properties |
| 2 | [16, 1, 240, 1]1⋅16 + 1⋅240 | is noble |
| 2 | [16, 1, 240, 1]1⋅16 + 1⋅240 | is linear |
| 2 | [16, 1, 240, 1]1⋅16 + 1⋅240 | is self-dual |
| 2 | [20, 1, 236, 1]1⋅20 + 1⋅236 | is monotonic |
| 2 | [24, 1, 232, 1]1⋅24 + 1⋅232 | is dense |
| 2 | [57, 1, 199, 1]1⋅57 + 1⋅199 | is honest |
| 2 | [62, 1, 194, 1]1⋅62 + 1⋅194 | is blotless |
| 2 | [64, 1, 192, 1]1⋅64 + 1⋅192 | great quaestor dominion |
| 2 | [64, 1, 192, 1]1⋅64 + 1⋅192 | great quaestor sword dominion |
| 2 | [66, 1, 190, 1]1⋅66 + 1⋅190 | is bloatless |
| 2 | [96, 1, 160, 1]1⋅96 + 1⋅160 | is blightless |
| 2 | [97, 1, 159, 1]1⋅97 + 1⋅159 | is male |
| 2 | [104, 1, 152, 1]1⋅104 + 1⋅152 | is in monotonic equivalence class |
| 2 | [128, 2]2⋅128 | is acute |
| 2 | [128, 2]2⋅128 | is odd |
| 2 | [128, 2]2⋅128 | is odious |
| 2 | [128, 2]2⋅128 | is ugly |
| 2 | [128, 2]2⋅128 | is rough |
| 2 | [128, 2]2⋅128 | is sharp |
| 2 | [128, 2]2⋅128 | is solid |
| 2 | [128, 2]2⋅128 | twin prefect oddnessZhegalkin deviation patron |
| 2 | [128, 2]2⋅128 | Zhegalkin deviation is odious |
| 2 | [128, 2]2⋅128 | is rude |
| 2 | [128, 2]2⋅128 | prefect oddness |
| 3 | [16, 1, 96, 1, 144, 1]1⋅16 + 1⋅96 + 1⋅144 | faction size |
| 3 | [16, 1, 112, 1, 128, 1]1⋅16 + 1⋅112 + 1⋅128 | nonlinearity |
| 3 | [32, 1, 96, 1, 128, 1]1⋅32 + 1⋅96 + 1⋅128 | village size |
| 3 | [40, 1, 57, 1, 159, 1]1⋅40 + 1⋅57 + 1⋅159 | honesty and gender |
| 3 | [58, 1, 70, 1, 128, 1]1⋅58 + 1⋅70 + 1⋅128 | sharpness and introversion |
| 3 | [80, 2, 96, 1]2⋅80 + 1⋅96 | super great banner |
| 4 | [2, 1, 6, 1, 30, 1, 218, 1]1⋅2 + 1⋅6 + 1⋅30 + 1⋅218 | valency |
| 4 | [2, 1, 6, 1, 30, 1, 218, 1]1⋅2 + 1⋅6 + 1⋅30 + 1⋅218 | soft gravitysoft legion factionsoft legion weight |
| 4 | [2, 1, 14, 1, 56, 1, 184, 1]1⋅2 + 1⋅14 + 1⋅56 + 1⋅184 | senior village size |
| 4 | [2, 1, 14, 1, 56, 1, 184, 1]1⋅2 + 1⋅14 + 1⋅56 + 1⋅184 | strengthfamily size |
| 4 | [2, 1, 14, 1, 56, 1, 184, 1]1⋅2 + 1⋅14 + 1⋅56 + 1⋅184 | soft depthsoft cohort weight |
| 4 | [2, 2, 12, 1, 240, 1]2⋅2 + 1⋅12 + 1⋅240 | adicity |
| 4 | [4, 1, 12, 1, 60, 1, 180, 1]1⋅4 + 1⋅12 + 1⋅60 + 1⋅180 | chain length |
| 4 | [4, 1, 28, 2, 196, 1]1⋅4 + 2⋅28 + 1⋅196 | twin-chunky twist partition |
| 4 | [16, 1, 80, 3]1⋅16 + 3⋅80 | anchor |
| 4 | [16, 1, 80, 3]1⋅16 + 3⋅80 | reduced chain quadrantstwin mentors of reduced chain quadrants |
| 4 | [32, 2, 96, 2]2⋅32 + 2⋅96 | quaestor sword dominion |
| 4 | [32, 2, 96, 2]2⋅32 + 2⋅96 | great patron dominion |
| 4 | [32, 2, 96, 2]2⋅32 + 2⋅96 | great patron principality |
| 4 | [32, 2, 96, 2]2⋅32 + 2⋅96 | consul weight |
| 4 | [32, 2, 96, 2]2⋅32 + 2⋅96 | prefect weight |
| 4 | [64, 4]4⋅64 | great patronpatron tiling and slattingpatron symmetry perm |
| 4 | [64, 4]4⋅64 | great quaestorquaestor tiling and slattingtwist xors 2 |
| 4 | [64, 4]4⋅64 | great prefect |
| 4 | [64, 4]4⋅64 | great praetor |
| 4 | [64, 4]4⋅64 | quadrant |
| 4 | [64, 4]4⋅64 | lictor |
| 4 | [64, 4]4⋅64 | lictor sword |
| 4 | [64, 4]4⋅64 | praetor shield |
| 4 | [64, 4]4⋅64 | reverse lictor |
| 4 | [64, 4]4⋅64 | nameless 5 |
| 4 | [64, 4]4⋅64 | weight quadrant |
| 4 | [64, 4]4⋅64 | guardian |
| 4 | [64, 4]4⋅64 | patron index consul |
| 4 | [64, 4]4⋅64 | serration 2 (half sharpness) |
| 5 | [1, 1, 15, 1, 48, 1, 64, 1, 128, 1]1⋅1 + 1⋅15 + 1⋅48 + 1⋅64 + 1⋅128 | serration size |
| 5 | [1, 1, 16, 1, 49, 1, 78, 1, 112, 1]1⋅1 + 1⋅16 + 1⋅49 + 1⋅78 + 1⋅112 | twist partition size |
| 5 | [1, 2, 6, 1, 30, 1, 218, 1]2⋅1 + 1⋅6 + 1⋅30 + 1⋅218 | gravitylegion weightlegion faction |
| 5 | [1, 2, 14, 1, 56, 1, 184, 1]2⋅1 + 1⋅14 + 1⋅56 + 1⋅184 | depthcohort weight |
| 5 | [1, 2, 14, 1, 112, 1, 128, 1]2⋅1 + 1⋅14 + 1⋅112 + 1⋅128 | twist level |
| 5 | [2, 2, 56, 2, 140, 1]2⋅2 + 2⋅56 + 1⋅140 | changes |
| 5 | [16, 1, 48, 3, 96, 1]1⋅16 + 3⋅48 + 1⋅96 | symmetry permsymmetry perm indices |
| 5 | [16, 2, 48, 2, 128, 1]2⋅16 + 2⋅48 + 1⋅128 | tribe |
| 5 | [16, 2, 64, 2, 96, 1]2⋅16 + 2⋅64 + 1⋅96 | quaestor weight |
| 5 | [16, 2, 64, 2, 96, 1]2⋅16 + 2⋅64 + 1⋅96 | praetor weight |
| 5 | [16, 2, 64, 2, 96, 1]2⋅16 + 2⋅64 + 1⋅96 | patron index weight |
| 5 | [16, 2, 64, 2, 96, 1]2⋅16 + 2⋅64 + 1⋅96 | sub-prefect weight |
| 5 | [16, 2, 64, 2, 96, 1]2⋅16 + 2⋅64 + 1⋅96 | Zhegalkin deviation weight |
| 5 | [40, 4, 96, 1]4⋅40 + 1⋅96 | great banner |
| 6 | [1, 3, 7, 2, 239, 1]3⋅1 + 2⋅7 + 1⋅239 | pure twist level |
| 6 | [16, 5, 176, 1]5⋅16 + 1⋅176 | patron symmetry neg |
| 7 | [1, 1, 6, 1, 8, 1, 25, 1, 32, 1, 56, 1, 128, 1]1⋅1 + 1⋅6 + 1⋅8 + 1⋅25 + 1⋅32 + 1⋅56 + 1⋅128 | honesty, gender, sharpness, introversion |
| 7 | [2, 2, 8, 1, 12, 1, 40, 1, 48, 1, 144, 1]2⋅2 + 1⋅8 + 1⋅12 + 1⋅40 + 1⋅48 + 1⋅144 | clan size |
| 7 | [5, 1, 20, 1, 29, 1, 36, 1, 46, 1, 60, 2]1⋅5 + 1⋅20 + 1⋅29 + 1⋅36 + 1⋅46 + 2⋅60 | nonmonotonicity |
| 7 | [8, 1, 24, 3, 48, 1, 56, 1, 72, 1]1⋅8 + 3⋅24 + 1⋅48 + 1⋅56 + 1⋅72 | super chunky burden |
| 7 | [16, 2, 32, 3, 64, 2]2⋅16 + 3⋅32 + 2⋅64 | village columnsvillage minrep |
| 8 | [2, 2, 6, 2, 8, 1, 24, 2, 184, 1]2⋅2 + 2⋅6 + 1⋅8 + 2⋅24 + 1⋅184 | soft cohort faction |
| 8 | [2, 4, 10, 3, 218, 1]4⋅2 + 3⋅10 + 1⋅218 | atomvals |
| 8 | [2, 4, 10, 3, 218, 1]4⋅2 + 3⋅10 + 1⋅218 | soft legionsoft legion set |
| 8 | [4, 1, 12, 1, 20, 3, 60, 3]1⋅4 + 1⋅12 + 3⋅20 + 3⋅60 | chain quadrantstwin mentors of chain quadrants |
| 8 | [8, 2, 24, 2, 48, 4]2⋅8 + 2⋅24 + 4⋅48 | company |
| 8 | [8, 2, 24, 4, 72, 2]2⋅8 + 4⋅24 + 2⋅72 | chunky twist vector |
| 8 | [16, 4, 48, 4]4⋅16 + 4⋅48 | quaestor dominion |
| 8 | [16, 4, 48, 4]4⋅16 + 4⋅48 | patron dominionpatron principalitypatron king index and quadrant |
| 8 | [16, 4, 48, 4]4⋅16 + 4⋅48 | Zhegalkin deviation factiontwin prefect signed weight |
| 8 | [16, 4, 48, 4]4⋅16 + 4⋅48 | prefect signed weight |
| 8 | [16, 4, 48, 4]4⋅16 + 4⋅48 | Zhegalkin linear signed weightreverse prefect signed weight |
| 8 | [32, 8]8⋅32 | quaestor sword |
| 8 | [32, 8]8⋅32 | super great twin mentorleveled praetor sword |
| 8 | [32, 8]8⋅32 | octant |
| 8 | [32, 8]8⋅32 | consul |
| 8 | [32, 8]8⋅32 | great sub-prefect |
| 8 | [32, 8]8⋅32 | twin consul |
| 8 | [32, 8]8⋅32 | twist xors 1 |
| 8 | [32, 8]8⋅32 | twist xors (2, 3) |
| 9 | [1, 2, 2, 1, 6, 2, 8, 1, 24, 2, 184, 1]2⋅1 + 1⋅2 + 2⋅6 + 1⋅8 + 2⋅24 + 1⋅184 | cohort faction |
| 9 | [1, 2, 2, 3, 10, 3, 218, 1]2⋅1 + 3⋅2 + 3⋅10 + 1⋅218 | legionlegion set |
| 9 | [1, 2, 8, 2, 28, 2, 56, 2, 70, 1]2⋅1 + 2⋅8 + 2⋅28 + 2⋅56 + 1⋅70 | weight |
| 9 | [1, 2, 8, 2, 28, 2, 56, 2, 70, 1]2⋅1 + 2⋅8 + 2⋅28 + 2⋅56 + 1⋅70 | zhegalkin weight |
| 10 | [16, 4, 32, 6]4⋅16 + 6⋅32 | chunky chain |
| 11 | [4, 2, 8, 2, 16, 2, 32, 3, 40, 1, 64, 1]2⋅4 + 2⋅8 + 2⋅16 + 3⋅32 + 1⋅40 + 1⋅64 | ultra clan |
| 11 | [4, 2, 12, 2, 16, 2, 24, 2, 48, 3]2⋅4 + 2⋅12 + 2⋅16 + 2⋅24 + 3⋅48 | great principality |
| 11 | [4, 2, 12, 2, 16, 2, 24, 2, 48, 3]2⋅4 + 2⋅12 + 2⋅16 + 2⋅24 + 3⋅48 | great dominion |
| 12 | [16, 8, 32, 4]8⋅16 + 4⋅32 | patron symmetry negperm |
| 13 | [4, 2, 8, 1, 12, 2, 24, 7, 48, 1]2⋅4 + 1⋅8 + 2⋅12 + 7⋅24 + 1⋅48 | platoon |
| 13 | [4, 2, 12, 6, 24, 2, 36, 2, 56, 1]2⋅4 + 6⋅12 + 2⋅24 + 2⋅36 + 1⋅56 | chunky burden |
| 14 | [2, 2, 6, 2, 8, 2, 16, 2, 24, 4, 48, 2]2⋅2 + 2⋅6 + 2⋅8 + 2⋅16 + 4⋅24 + 2⋅48 | super clan |
| 15 | [4, 4, 8, 6, 32, 4, 64, 1]4⋅4 + 6⋅8 + 4⋅32 + 1⋅64 | super guild reps |
| 16 | [1, 4, 7, 8, 49, 4]4⋅1 + 8⋅7 + 4⋅49 | twist partition |
| 16 | [1, 8, 2, 6, 4, 1, 232, 1]8⋅1 + 6⋅2 + 1⋅4 + 1⋅232 | noble symmetry neg |
| 16 | [2, 8, 8, 7, 184, 1]8⋅2 + 7⋅8 + 1⋅184 | symmetry negsymmetry neg indices |
| 16 | [2, 8, 8, 7, 184, 1]8⋅2 + 7⋅8 + 1⋅184 | soft cohortsoft cohort set |
| 16 | [4, 4, 12, 8, 36, 4]4⋅4 + 8⋅12 + 4⋅36 | twin-chunky twist vector |
| 16 | [16, 16]16⋅16 | nameless 1 |
| 16 | [16, 16]16⋅16 | prefect |
| 16 | [16, 16]16⋅16 | praetor |
| 16 | [16, 16]16⋅16 | quaestor |
| 16 | [16, 16]16⋅16 | patronpatron indexpraetor sword |
| 16 | [16, 16]16⋅16 | nameless 3 |
| 16 | [16, 16]16⋅16 | nameless 4 |
| 16 | [16, 16]16⋅16 | great twin mentor |
| 16 | [16, 16]16⋅16 | Zhegalkin linearreverse prefect |
| 16 | [16, 16]16⋅16 | Zhegalkin deviationtwin prefect |
| 16 | [16, 16]16⋅16 | chunky twist xorschunky seminar |
| 16 | [16, 16]16⋅16 | serration 1 (quarter sharpness) |
| 16 | [16, 16]16⋅16 | half sharpness and quadrant |
| 17 | [1, 2, 2, 7, 8, 7, 184, 1]2⋅1 + 7⋅2 + 7⋅8 + 1⋅184 | cohortcohort set |
| 18 | [4, 4, 8, 6, 16, 4, 32, 4]4⋅4 + 6⋅8 + 4⋅16 + 4⋅32 | ultra family |
| 20 | [4, 4, 12, 12, 24, 4]4⋅4 + 12⋅12 + 4⋅24 | squad |
| 20 | [8, 8, 16, 12]8⋅8 + 12⋅16 | noble symmetry perm |
| 20 | [10, 16, 24, 4]16⋅10 + 4⋅24 | banner |
| 22 | [1, 2, 2, 1, 4, 2, 6, 2, 8, 5, 12, 4, 24, 6]2⋅1 + 1⋅2 + 2⋅4 + 2⋅6 + 5⋅8 + 4⋅12 + 6⋅24 | clan |
| 28 | [1, 2, 2, 1, 4, 9, 8, 7, 16, 8, 32, 1]2⋅1 + 1⋅2 + 9⋅4 + 7⋅8 + 8⋅16 + 1⋅32 | guild reps |
| 30 | [2, 8, 8, 14, 16, 8]8⋅2 + 14⋅8 + 8⋅16 | super family |
| 32 | [8, 32]32⋅8 | sub-prefect |
| 32 | [8, 32]32⋅8 | super chunk |
| 32 | [8, 32]32⋅8 | twist xors (1, 2) |
| 37 | [2, 12, 4, 12, 8, 3, 10, 4, 20, 6]12⋅2 + 12⋅4 + 3⋅8 + 4⋅10 + 6⋅20 | symmetry negpermsymmetry negperm indices |
| 38 | [1, 8, 3, 14, 9, 8, 12, 4, 20, 2, 23, 2]8⋅1 + 14⋅3 + 8⋅9 + 4⋅12 + 2⋅20 + 2⋅23 | burden |
| 40 | [1, 4, 2, 6, 5, 12, 10, 18]4⋅1 + 6⋅2 + 12⋅5 + 18⋅10 | chain |
| 44 | [1, 8, 3, 8, 4, 8, 6, 8, 12, 12]8⋅1 + 8⋅3 + 8⋅4 + 8⋅6 + 12⋅12 | principality |
| 44 | [1, 8, 3, 8, 4, 8, 6, 8, 12, 12]8⋅1 + 8⋅3 + 8⋅4 + 8⋅6 + 12⋅12 | dominion |
| 46 | [1, 2, 2, 7, 4, 14, 8, 23]2⋅1 + 7⋅2 + 14⋅4 + 23⋅8 | family |
| 46 | [1, 2, 2, 7, 4, 14, 8, 23]2⋅1 + 7⋅2 + 14⋅4 + 23⋅8 | reverse familysenior village columns |
| 64 | [1, 16, 3, 32, 9, 16]16⋅1 + 32⋅3 + 16⋅9 | twist vectorreverse and twin prefect signed weight |
| 64 | [4, 64]64⋅4 | twin mentor |
| 64 | [4, 64]64⋅4 | chunk |
| 64 | [4, 64]64⋅4 | twist xors |
| 64 | [4, 64]64⋅4 | quarter sharpness and quadrant |
| 66 | [1, 28, 2, 18, 6, 8, 12, 12]28⋅1 + 18⋅2 + 8⋅6 + 12⋅12 | noble symmetry negperm |
| 80 | [1, 16, 3, 48, 6, 16]16⋅1 + 48⋅3 + 16⋅6 | faction |
| 96 | [2, 64, 4, 32]64⋅2 + 32⋅4 | seminar |
| 184 | [1, 124, 2, 48, 3, 12]124⋅1 + 48⋅2 + 12⋅3 | splinter |