Zobrazeno 1 - 10
of 30 261
pro vyhledávání: '"Binomial coefficients"'
Autor:
Chen, Chongyao, Wickelgren, Kirsten
We compute an analogue of Pascal's triangle enriched in bilinear forms over a finite field. This gives an arithmetically meaningful count of the ways to choose $j$ embeddings into an \'etale extension of degree $n$. We also compute a quadratic twist.
Externí odkaz:
http://arxiv.org/abs/2412.14277
Autor:
Hwang, WonTae, Song, Kyunghwan
The greatest integer that does not belong to a numerical semigroup $S$ is called the Frobenius number of $S$, and finding the Frobenius number is called the Frobenius problem. In this paper, we solve the Frobenius problem for Binomial Coefficients.
Externí odkaz:
http://arxiv.org/abs/2412.17882
Autor:
Li, Chunli1 (AUTHOR), Chu, Wenchang1 (AUTHOR) hypergeometricx@outlook.com
Publikováno v:
Mathematical Notes. Dec2023, Vol. 114 Issue 5/6, p1306-1313. 8p.
The summatory function of the number of binomial coefficients not divisible by a prime is known to exhibit regular periodic oscillations, yet identifying the less regularly behaved minimum of the underlying periodic functions has been open for almost
Externí odkaz:
http://arxiv.org/abs/2408.06817
Publikováno v:
Applied Mathematics in Science & Engineering. Dec2023, Vol. 31 Issue 1, p1-12. 12p.
Autor:
Lupu, Cezar, Matei, Vlad
In this note, we give an exact formula for a general family of rational zeta series involving the coefficient $\zeta(2n)$ in terms of Hurwitz zeta values. This formula generalizes two formulas from a previous paper of the first author. Our method wil
Externí odkaz:
http://arxiv.org/abs/2409.16187
Autor:
Cigler, Johann
We obtain formulas for the coefficients of positive and negative powers of a partial theta function.
Comment: 5 pages
Comment: 5 pages
Externí odkaz:
http://arxiv.org/abs/2408.14094
Autor:
Küstner, Josef1 (AUTHOR), Schlosser, Michael J.1 (AUTHOR), Yoo, Meesue2 (AUTHOR) meesueyoo@chungbuk.ac.kr
Publikováno v:
Annals of Combinatorics. Dec2023, Vol. 27 Issue 4, p917-955. 39p.
Autor:
Pain, Jean-Christophe
Recently, Agievich proposed an interesting upper bound on binomial coefficients in the de Moivre-Laplace form. In this article, we show that the latter bound, in the specific case of a central binomial coefficient, is larger than the one proposed by
Externí odkaz:
http://arxiv.org/abs/2407.21064
Autor:
Segun, Akerele Olofin
We find various series that involves the central binomial coefficients $\binom{2n}{n}$, harmonic numbers and Fibonacci Numbers.\\ Contrary to the traditional hypergeometric function $_pF_q$ approach, our method utilizes a straightforward transformati
Externí odkaz:
http://arxiv.org/abs/2405.16814