As we have empirically observed but not explicitly stated so far and implicitly assumed, a condition for a valid abbreviation may be that the indices of the letters must maintain ascending order, or, in other words, the original sequence of the letters is not permuted. If so, for each word length <hi xmlns="http://www.tei-c.org/ns/1.0" rend="italic">w </hi>and abbreviation length <hi xmlns="http://www.tei-c.org/ns/1.0" rend="italic">a </hi>there are { <hi xmlns="http://www.tei-c.org/ns/1.0" rend="italic">w </hi> <hi xmlns="http://www.tei-c.org/ns/1.0" rend="italic">/</hi> <hi xmlns="http://www.tei-c.org/ns/1.0" rend="italic">choose a</hi> <hi xmlns="http://www.tei-c.org/ns/1.0" rend="italic">}</hi> <hi xmlns="http://www.tei-c.org/ns/1.0" rend="italic"> <ref target="ftn7" n="7" /> </hi> possible abbreviations, since for each distinct combination only one can maintain the ascending order of elements. Now in order for understanding how many possible abbreviations there are for each word we need to add up values for all different <hi xmlns="http://www.tei-c.org/ns/1.0" rend="italic">a</hi>, where <hi xmlns="http://www.tei-c.org/ns/1.0" rend="italic"> a &lt; w</hi>. <ref xmlns="http://www.tei-c.org/ns/1.0" target="ftn8" n="8" />