1 Le cas des motifs auto-maximaux

𝑝 𝑢 ∀𝑖∈ {1,...,∣𝑢∣−𝑝}, 𝑢[𝑖] =
𝑢[𝑖+𝑝]Period(𝑢)𝑢
∣𝑢∣𝑢 𝑢 Period(𝑢)≤
∣𝑢∣/2
𝑝 𝑞 𝑢 𝑝 +𝑞 <
∣𝑢∣pgcd(𝑝, 𝑞)𝑢
MaxSuf (𝑤)
𝑤 𝑤
MaxSuf (𝑤) = 𝑤
𝑤Period(MaxSuf (𝑤)) = Period(𝑤)
𝑤
𝑤 𝑗
Period
𝑖 𝑗
𝑤[𝑖]∕=𝑤[𝑖−Period]Period 𝑖
Period
𝑤 𝑤 𝑗
Period(𝑤[1, 𝑗]) 𝑝=Period (𝑤[1, 𝑖−
1]) 𝑤[𝑖]∕=𝑤[𝑖−𝑝]𝑤[𝑖]< 𝑤[𝑖−𝑝]
Period(𝑤[1, 𝑖]) < 𝑖
𝑃
𝜋
𝑃 𝑗 >
0𝑗−𝜋(𝑗) = Period(𝑃[1, 𝑗])

𝑃
𝑃=𝑢𝑣 𝑣 =MaxSuf (𝑃)
𝑃
𝑣 𝑖 𝑇 𝑢𝑣
𝑗 𝑇 𝑗 ∈ {𝑖− ∣𝑢∣+ 1, 𝑖 − ∣𝑢∣+ 2, . . . , 𝑖}
∣𝑇∣
MaxSuf (𝑃)
𝑤
𝑤
Period
𝑖∣𝑤∣
𝑤[𝑖]< 𝑤[𝑖−Period]Period 𝑖
𝑤[𝑖]> 𝑤[𝑖−Period]
(𝑖−1,Period)
(∣𝑤∣,Period)
𝑤
𝑤
MaxSuf (𝑃)
2⋅ ∣𝑃∣
𝑛
𝑢 𝑛 𝑢(𝑖)=𝑢[𝑖+ 1, 𝑛]𝑢[1, 𝑖]
𝑢 𝑣 𝑖 𝑗
𝑢(𝑖)=𝑣(𝑗)
𝐷(𝑢) = {𝑘∈ {1, . . . , 𝑛}∣∃𝑗, 𝑢(𝑘)> 𝑣(𝑗)}
𝐷(𝑣) = {𝑘∈ {1, . . . , 𝑛}∣∃𝑗, 𝑣(𝑘)> 𝑢(𝑗)}
𝐷(𝑢) = {1, . . . , 𝑛}𝐷(𝑣) = {1, . . . , 𝑛}𝑢 𝑣