John Solutions

Pascal’s Triangle

  5{(0,x)+x,0}\1

Dereplicated Map (oK, k3)

  f: {(x'y)(y:?y)?/:y}

2x2 Matrix Determinant

  f: {-/x*|y}.

Longest Cycle Count

  f: |/#:'{x\'x}@  

Rising Edge

  f:0>':

Sign

  f: {(0<x)-x<0}

Find a Function’s Name

  f: {$(t[0],_n)@(t:+..k)[1]?x}

Is Inverleave?

  f: {y~z@&~':x{:[y~*x;1_ x;x]}\z}

Merge Dictionaries

  f:{.+(k;({x@&~_n~/:x}x@')'k:?,/!:'x)}

Distinct Names

  f:{x,'(,/($!#:)'t)@<,/t:=x}

Limit Run Length

  f: {y@&~x<{y*x+y}\z=y}