Wednesday, July 09, 2014

Is there a word for the top part of a binomial coefficient?

Consider the sequence:

x/y,  (x+1)/y, (x+2)/y, ..., (x+z)/y

one could say  in this sequence of fractions the numerators goes through z-1 consecutive numbers.

Consider the sequence

(x choose y), (x+1 choose y), (x+2 choose y),...,(x+z choose y)

one could say in this sequence of binomial coefficients the top-part goes through z-1 consecutive numbers.

Is there a better way to say this? That is, is there a term for the top-part of a binomial coefficient? Or for that matter the bottom part? I have not been able to find one on the web. Hence I propose a contest:

  1. Leave as a comment a proposed name for the top-part and for the bottom-part of a binomial coefficient.
  2. If you find a website that has some official name, leave that as a comment.
I am not sure if there will be a winner of what he or she will get. But if we can agree upon a term then we are all winners!


  1. Considering it's a binomial coefficient, perhaps the top part should be called the degree (it represents the coefficients of a homogeneous polynomial of a fixed degree, after all). For the bottom, how about index? As in, the index of the term that the binomial coefficient is for in the corresponding lex order on the terms.

  2. Lets call upper part bino and lower part mial. Just like bra - ket

  3. Isn't it called numerator and denominator?

  4. In your initial sequence I would say that the numerators go through (z+1) consecutive integers actually.
    For the binomial coefficients I would probably stick with the (mostly standard) "outcomes" and "possibilities" ( ) since most people encounter them first during Combinatorics.

  5. For the top: "binomerator".

    For the bottom... I've got nothing.

  6. choosand / choosee / chooser / ...

    Now just decide which is which :)

  7. I like just using numerator and denominator

  8. I have to agree with Anonymous here --- we can make up all sorts of cute names, but if we had a serious paper where we actually wanted the reader to understand what was going on, we had best them call the "numerator" and "denominator" of the binomial coefficient.

  9. Set size and subset size.