LaTeX errors when creating PDF version.
This typically indicates Rd problems.
LaTeX errors found:
! LaTeX Error: Environment aligned undefined.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
! Misplaced alignment tab character &.
<argument>  \begin {aligned} 2^N &
                                  = \lbrace 123, 12, 13, 23, 1, 2, 3, \empty...
l.86 }{}
        
! Misplaced alignment tab character &.
<argument> ... \emptyset \rbrace \\ \mathcal {P} &
                                                  = \lbrace 12, 13, 1, 2 \rb...
l.86 }{}
        
! Misplaced alignment tab character &.
<argument> ...race \\ 2^N \setminus \mathcal {P} &
                                                  = \lbrace 123, 23, 3, \emp...
l.86 }{}
        
! LaTeX Error: \begin{list} on input line 65 ended by \end{aligned}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
! LaTeX Error: Environment bmatrix undefined.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
! Misplaced alignment tab character &.
<argument>  M^\succeq _1 = \begin {bmatrix} 0 &
                                                1 & 0\\ 1 & 1 & 0\\ 1 & 0 & ...
l.1301 }{}
          
! Misplaced alignment tab character &.
<argument> ...succeq _1 = \begin {bmatrix} 0 & 1 &
                                                   0\\ 1 & 1 & 0\\ 1 & 0 & 0...
l.1301 }{}
          
! Misplaced alignment tab character &.
<argument> ...1 = \begin {bmatrix} 0 & 1 & 0\\ 1 &
                                                   1 & 0\\ 1 & 0 & 0 \end {b...
l.1301 }{}
          
! Misplaced alignment tab character &.
<argument> ...\begin {bmatrix} 0 & 1 & 0\\ 1 & 1 &
                                                   0\\ 1 & 0 & 0 \end {bmatr...
l.1301 }{}
          
! Misplaced alignment tab character &.
<argument> ...bmatrix} 0 & 1 & 0\\ 1 & 1 & 0\\ 1 &
                                                   0 & 0 \end {bmatrix} M^\s...
l.1301 }{}
          
! Misplaced alignment tab character &.
<argument> ...rix} 0 & 1 & 0\\ 1 & 1 & 0\\ 1 & 0 &
                                                   0 \end {bmatrix} M^\succe...
l.1301 }{}
          
! LaTeX Error: \begin{list} on input line 1270 ended by \end{bmatrix}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
! LaTeX Error: Environment bmatrix undefined.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
! Misplaced alignment tab character &.
<argument> ... M^\succeq _2 = \begin {bmatrix} 1 &
                                                   0 & 0\\ 0 & 1 & 1\\ 1 & 0...
l.1301 }{}
          
! Misplaced alignment tab character &.
<argument> ...succeq _2 = \begin {bmatrix} 1 & 0 &
                                                   0\\ 0 & 1 & 1\\ 1 & 0 & 0...
l.1301 }{}
          
! Misplaced alignment tab character &.
<argument> ...2 = \begin {bmatrix} 1 & 0 & 0\\ 0 &
                                                   1 & 1\\ 1 & 0 & 0 \end {b...
l.1301 }{}
          
! Misplaced alignment tab character &.
<argument> ...\begin {bmatrix} 1 & 0 & 0\\ 0 & 1 &
                                                   1\\ 1 & 0 & 0 \end {bmatr...
l.1301 }{}
          
! Misplaced alignment tab character &.
<argument> ...bmatrix} 1 & 0 & 0\\ 0 & 1 & 1\\ 1 &
                                                   0 & 0 \end {bmatrix} M^\s...
l.1301 }{}
          
! Misplaced alignment tab character &.
<argument> ...rix} 1 & 0 & 0\\ 0 & 1 & 1\\ 1 & 0 &
                                                   0 \end {bmatrix} M^\succe...
l.1301 }{}
          
! LaTeX Error: \begin{list} on input line 1270 ended by \end{bmatrix}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
! LaTeX Error: Environment bmatrix undefined.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
! Misplaced alignment tab character &.
<argument> ... M^\succeq _3 = \begin {bmatrix} 0 &
                                                   1 & 0\\ 1 & 0 & 1\\ 1 & 0...
l.1301 }{}
          
! Misplaced alignment tab character &.
<argument> ...succeq _3 = \begin {bmatrix} 0 & 1 &
                                                   0\\ 1 & 0 & 1\\ 1 & 0 & 0...
l.1301 }{}
          
! Misplaced alignment tab character &.
<argument> ...3 = \begin {bmatrix} 0 & 1 & 0\\ 1 &
                                                   0 & 1\\ 1 & 0 & 0 \end {b...
l.1301 }{}
          
! Misplaced alignment tab character &.
<argument> ...\begin {bmatrix} 0 & 1 & 0\\ 1 & 0 &
                                                   1\\ 1 & 0 & 0 \end {bmatr...
l.1301 }{}
          
! Misplaced alignment tab character &.
<argument> ...bmatrix} 0 & 1 & 0\\ 1 & 0 & 1\\ 1 &
                                                   0 & 0 \end {bmatrix} 
l.1301 }{}
          
! Misplaced alignment tab character &.
<argument> ...rix} 0 & 1 & 0\\ 1 & 0 & 1\\ 1 & 0 &
                                                   0 \end {bmatrix} 
l.1301 }{}
          
! LaTeX Error: \begin{list} on input line 1270 ended by \end{bmatrix}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
! Undefined control sequence.
<argument> ...1}{k!}\sum _{j=0}^{k} (-1)^j \binom 
                                                  {k}{j}(k-j)^n
l.1937 ..._{j=0}^{k} (-1)^j \binom{k}{j}(k-j)^n}{}