Merges

Counting Adjacent Pairs

The first calculation is an integer pair-count table. Frequencies weight each adjacent occurrence, so the displayed corpus determines every count.

highlighted = computed this step

Counting adjacent pairs

A pair count is the sum over words of frequency times adjacent occurrences. Every count is an integer because the corpus frequencies and occurrences are integers.

pair count=∑freq⋅adjacent occurrences\text{pair count}=\sum \text{freq}\cdot\text{adjacent occurrences}
Round one pair countsAdjacent pair counts are exact integers.Round one pair countsAdjacent pair counts are exact integers.round one countstie-break: lexicographically smallest pair among max countscurrent corpushug freq=3 symbols=h u gpug freq=2 symbols=p u gpair counts(h,u)=3(p,u)=2(u,g)=5

Round one counts

From the shown corpus, (h,u) has count 3, (u,g) has count 5, and (p,u) has count 2.

(h,u)=3,(u,g)=5,(p,u)=2(h,u)=3,\quad (u,g)=5,\quad (p,u)=2
Round one pair countsAdjacent pair counts are exact integers.Round one pair countsAdjacent pair counts are exact integers.round one countstie-break: lexicographically smallest pair among max countscurrent corpushug freq=3 symbols=h u gpug freq=2 symbols=p u gpair counts(h,u)=3(p,u)=2(u,g)=5

Summary

The largest count is attached to (u,g). The next step applies the deterministic merge rule to that exact maximum.

max⁡{3,5,2}=5\max\{3,5,2\}=5
Round one pair countsAdjacent pair counts are exact integers.Round one pair countsAdjacent pair counts are exact integers.round one countstie-break: lexicographically smallest pair among max countscurrent corpushug freq=3 symbols=h u gpug freq=2 symbols=p u gpair counts(h,u)=3(p,u)=2(u,g)=5