Template:Boolf weight triangle 4

rational weight

w a $0$ ${\frac {1}{16}}$ ${\frac {1}{8}}$ ${\frac {3}{16}}$ ${\frac {1}{4}}$ ${\frac {5}{16}}$ ${\frac {3}{8}}$ ${\frac {7}{16}}$ ${\frac {1}{2}}$ ${\frac {9}{16}}$ ${\frac {5}{8}}$ ${\frac {11}{16}}$ ${\frac {3}{4}}$ ${\frac {13}{16}}$ ${\frac {7}{8}}$ ${\frac {15}{16}}$ $1$ sums 0 {{{1}}} {{{2}}} 1 {{{3}}} {{{4}}} {{{5}}} 2 {{{6}}} {{{7}}} {{{8}}} {{{9}}} {{{10}}} 3 {{{11}}} {{{12}}} {{{13}}} {{{14}}} {{{15}}} {{{16}}} {{{17}}} {{{18}}} {{{19}}} 4 {{{20}}} {{{21}}} {{{22}}} {{{23}}} {{{24}}} {{{25}}} {{{26}}} {{{27}}} {{{28}}} {{{29}}} {{{30}}} {{{31}}} {{{32}}} {{{33}}} {{{34}}} {{{35}}} {{{36}}}

integer weight
w a 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 sums 0 {{{1}}} {{{2}}} 1 {{{3}}} {{{4}}} {{{5}}} 2 {{{6}}} {{{7}}} {{{8}}} {{{9}}} {{{10}}} 3 {{{11}}} {{{12}}} {{{13}}} {{{14}}} {{{15}}} {{{16}}} {{{17}}} {{{18}}} {{{19}}} 4 {{{20}}} {{{21}}} {{{22}}} {{{23}}} {{{24}}} {{{25}}} {{{26}}} {{{27}}} {{{28}}} {{{29}}} {{{30}}} {{{31}}} {{{32}}} {{{33}}} {{{34}}} {{{35}}} {{{36}}}

merged integer weights
w 0 1 2 3...4 5...8 9...16 sums k a -1 0 1 2 3 4 0 {{{1}}} {{{2}}} 1 {{{3}}} {{{4}}} {{{5}}} 2 {{{6}}} {{{7}}} {{{8}}} 3 {{{11}}} {{{12}}} {{{13}}} 4 {{{20}}} {{{21}}} {{{22}}}

(plain text)

rows: [{{{1}}}, {{{2}}}], [{{{3}}}, {{{4}}}, {{{5}}}], [{{{6}}}, {{{7}}}, {{{8}}}, {{{9}}}, {{{10}}}], [{{{11}}}, {{{12}}}, {{{13}}}, {{{14}}}, {{{15}}}, {{{16}}}, {{{17}}}, {{{18}}}, {{{19}}}], [{{{20}}}, {{{21}}}, {{{22}}}, {{{23}}}, {{{24}}}, {{{25}}}, {{{26}}}, {{{27}}}, {{{28}}}, {{{29}}}, {{{30}}}, {{{31}}}, {{{32}}}, {{{33}}}, {{{34}}}, {{{35}}}, {{{36}}}] central values:   (rational weight = 1/2) [{{{4}}}, {{{8}}}, {{{15}}}, {{{28}}}] diagonal:   (integer weight = arity) [{{{1}}}, {{{4}}}, {{{8}}}, {{{14}}}, {{{24}}}] row sums: [, , , , ] merged rows: [{{{1}}}, {{{2}}}], [{{{3}}}, {{{4}}}, {{{5}}}], [{{{6}}}, {{{7}}}, {{{8}}}, ], [{{{11}}}, {{{12}}}, {{{13}}}, , ], [{{{20}}}, {{{21}}}, {{{22}}}, , , ] merged diagonal:   (k = arity) [{{{2}}}, {{{5}}}, , , ]

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see e.g. {{Boolf weight triangle; male}}

{{Boolf weight triangle 5}} is for arities up to 5.