Combinatorial Analysis - 26.4 Lattice Paths: Multinomial Coefficients and Set Partitions
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
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| 26.4.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \multinomial{n_{1}+n_{2}}{n_{1},n_{2}} = \binom{n_{1}+n_{2}}{n_{1}}}
\multinomial{n_{1}+n_{2}}{n_{1},n_{2}} = \binom{n_{1}+n_{2}}{n_{1}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | multinomial(n[1]+ n[2], n[1], n[2]) = binomial(n[1]+ n[2],n[1])
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Multinomial[Subscript[n, 1]+ Subscript[n, 2]] == Binomial[Subscript[n, 1]+ Subscript[n, 2],Subscript[n, 1]]
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Failure | Failure | Error | Failed [100 / 100]
Result: Complex[-0.4855310647423219, -0.7913166384345096]
Test Values: {Rule[Subscript[n, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[n, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Complex[0.5823425344168771, -0.5778520047366285]
Test Values: {Rule[Subscript[n, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[n, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
... skip entries to safe data |
| 26.4.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \binom{n_{1}+n_{2}}{n_{1}} = \binom{n_{1}+n_{2}}{n_{2}}}
\binom{n_{1}+n_{2}}{n_{1}} = \binom{n_{1}+n_{2}}{n_{2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | binomial(n[1]+ n[2],n[1]) = binomial(n[1]+ n[2],n[2])
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Binomial[Subscript[n, 1]+ Subscript[n, 2],Subscript[n, 1]] == Binomial[Subscript[n, 1]+ Subscript[n, 2],Subscript[n, 2]]
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Failure | Successful | Error | Failed [6 / 100]
Result: Indeterminate
Test Values: {Rule[Subscript[n, 1], -1.5], Rule[Subscript[n, 2], -1.5]}
Result: Indeterminate
Test Values: {Rule[Subscript[n, 1], -1.5], Rule[Subscript[n, 2], -0.5]}
... skip entries to safe data |