On sums of binomial coefficients and their applications
| dc.creator | Sun, Zhi-Wei | |
| dc.date | 2004-04-21 | |
| dc.date | 2008-07-14 | |
| dc.date.accessioned | 2026-07-07T09:49:54Z | |
| dc.date.available | 2026-07-07T09:49:54Z | |
| dc.description | In this paper we study recurrences concerning the combinatorial sum $[n,r]_m=\sum_{k\equiv r (mod m)}\binom {n}{k}$ and the alternate sum $\sum_{k\equiv r (mod m)}(-1)^{(k-r)/m}\binom{n}{k}$, where m>0, $n\ge 0$ and r are integers. For example, we show that if $n\ge m-1$ then $$\sum_{i=0}^{\lfloor(m-1)/2\rfloor}(-1)^i\binom{m-1-i}i [n-2i,r-i]_m=2^{n-m+1}.$$ We also apply such results to investigate Bernoulli and Euler polynomials. Our approach depends heavily on an identity established by the author [Integers 2(2002)]. | |
| dc.identifier | https://arxiv.org/abs/math/0404385 | |
| dc.identifier | http://arxiv.org/abs/math/0404385 | |
| dc.identifier | Discrete Math. 308(2008), 4231-4245 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164760 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11B65, 05A19, 11B37, 11B68 | |
| dc.title | On sums of binomial coefficients and their applications | |
| dc.type | text |