to obtain from this model the gaussian binomial coefficient formula_6, it suffices to count each word with a factor , where is the number of "inversions" of the word: the number of pairs of positions for which the leftmost position of the pair holds a letter 1 and the rightmost position holds a letter 0 in the word. for example, there is one word with 0 inversions, 0011. there is 1 with only a single inversion, 0101. there are two words with 2 inversions, 0110, and 1001. there is one with 3, 1010, and finally one word with 4 inversions, 1100. this corresponds to the coefficients in formula_22.