Common substring with shifts in b-ary expansions
Denote by S n ( x , y ) the length of the longest common substring of x and y with shifts in their first n digits of the b -ary expansions. We show that the sets of pairs ( x , y ), for which the growth rate of S n ( x , y ) is α log n with 0 ≤ α ≤ ∞ , have full Hausdorff dimension. Our method reli...
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| Veröffentlicht in: | Archiv der Mathematik 2024-10, Vol.123 (4), p.369-377 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Denote by
S
n
(
x
,
y
)
the length of the longest common substring of
x
and
y
with shifts in their first
n
digits of the
b
-ary expansions. We show that the sets of pairs (
x
,
y
), for which the growth rate of
S
n
(
x
,
y
)
is
α
log
n
with
0
≤
α
≤
∞
, have full Hausdorff dimension. Our method relies upon some estimation of the spectral radius of matrices. |
|---|---|
| ISSN: | 0003-889X 1420-8938 |
| DOI: | 10.1007/s00013-024-02038-1 |