Concept

Lexicographic order

The order in which words appear in a dictionary: compare the first letters, and where they agree compare the next. It is used to pick a canonical representative from a collection of equivalent objects, because it costs nothing to state and two parties can arrive at the same one independently.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

The quietest loudest complaint in any two of three decide. The triangle of all splits of what a three-player group is worth, with the split minimising the largest excess marked, the average split beside it, and the loudest complaint named.

The objection nobody can make louder

When no split of the winnings survives every group's objection, the core is empty and the question changes — which split makes the loudest objection as quiet as it can be? Sorting the complaints and minimising them in dictionary order picks exactly one split, always, whether or not the core exists.

applied · the core

6 necklaces, concatenated into a de Bruijn sequence. The Lyndon words of length dividing 4 over 2 letters, listed in lexicographic order and written end to end; the result is the lexicographically least de Bruijn sequence of order 4.

Every necklace, in order

The graph construction needs the whole graph in memory and finds one sequence among hundreds of millions. Listing the necklaces in alphabetical order and writing them end to end needs no graph at all, and produces the smallest of them.

computation · de bruijn

Named alongside it

The objects these essays reach for when they reach for this one.

Balancedness Coalition Core Counting argument De bruijn sequence Equivalence class Eulerian path Excess Greedy algorithm Imputation Lyndon word Necklace

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