The Distribution of the Carlitz Binomial Coefficients Modulo a Prime
For a nonnegative integer n , and a prime P in F q [ T ] , we prove a result that provides a method for computing the number of integers m with 0 ≤ m ≤ n for which the Carlitz binomial coefficients ( m n ) C fall into each of the residue classes modulo P . Our main result can be viewed as a function...
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| Veröffentlicht in: | Annals of combinatorics 2018-09, Vol.22 (3), p.601-617 |
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| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | For a nonnegative integer
n
, and a prime
P
in
F
q
[
T
]
, we prove a result that provides a method for computing the number of integers m with
0
≤
m
≤
n
for which the Carlitz binomial coefficients
(
m
n
)
C
fall into each of the residue classes modulo
P
. Our main result can be viewed as a function field analogue of the Garfield-Wilf theorem. |
|---|---|
| ISSN: | 0218-0006 0219-3094 |
| DOI: | 10.1007/s00026-018-0400-6 |