Zobrazeno 1 - 10
of 79
pro vyhledávání: '"Zhou, Nian Hong"'
Autor:
Schlosser, Michael J., Zhou, Nian Hong
We prove specific biases in the number of occurrences of parts belonging to two different residue classes $a$ and $b$, modulo a fixed non-negative integer $m$, for the sets of unrestricted partitions, partitions into distinct parts, and overpartition
Externí odkaz:
http://arxiv.org/abs/2408.14365
Autor:
Zhou, Nian Hong
In this paper, we examine the unimodality and strict unimodality of certain formal bivariate Laurent series with non-negative coefficients. We show that the sets of these formal bivariate Laurent series form commutative semirings under the operations
Externí odkaz:
http://arxiv.org/abs/2408.04433
Autor:
Zhou, Nian Hong
In this paper, we refine a result of Andrews and Merca on truncated pentagonal number series. Subsequently, we establish some positivity results involving Andrews--Gordon--Bressoud identities and $d$-regular partitions. In particular, we prove severa
Externí odkaz:
http://arxiv.org/abs/2403.06196
Autor:
Schlosser, Michael J., Zhou, Nian Hong
Motivated by recent work of George Andrews and Mircea Merca on the expansion of the quotient of the truncation of Euler's pentagonal number series by the complete series, we provide similar expansion results for averages involving truncations of sele
Externí odkaz:
http://arxiv.org/abs/2307.10821
Autor:
Zhou, Nian Hong
Let $\beta>1$ be fixed. We consider the $(\frak{b, d})$ numeration system, where the base ${\frak b}=(b_k)_{k\geq 0}$ is a sequence of positive real numbers satisfying $\lim_{k\rightarrow \infty}b_{k+1}/b_k=\beta$, and the set of digits ${\frak d}\ni
Externí odkaz:
http://arxiv.org/abs/2305.00792
Autor:
Zhou, Nian Hong
Let $N_k(m,n)$ denote the number of partitions of $n$ with Garvan $k$-rank $m$. It is well-known that Andrews-Garvan-Dyson's crank and Dyson's rank are the $k$-rank for $k=1$ and $k=2$, respectively. In this paper, we prove that the sequence $\{N_k(m
Externí odkaz:
http://arxiv.org/abs/2110.11174
Autor:
Zhou, Nian Hong, Niu, Da-Wei
In this paper we investigate the monotonicity properties related to the ratio of gamma functions, from which some related asymptotics and inequalities are established. Some special cases also confirm the conjectures of C.-P. Chen [Monotonicity proper
Externí odkaz:
http://arxiv.org/abs/2104.01880
Autor:
Zhou, Nian Hong, Li, Ya-Li
Let $\kappa$ be a positive real number and $m\in\mathbb{N}\cup\{\infty\}$ be given. Let $p_{\kappa, m}(n)$ denote the number of partitions of $n$ into the parts from the Piatestki-Shapiro sequence $(\lfloor \ell^{\kappa}\rfloor)_{\ell\in \mathbb{N}}$
Externí odkaz:
http://arxiv.org/abs/2104.01886
Autor:
Schlosser, Michael J., Zhou, Nian Hong
In this paper, we study properties of the coefficients appearing in the $q$-series expansion of $\prod_{n\ge 1}[(1-q^n)/(1-q^{pn})]^\delta$, the infinite Borwein product for an arbitrary prime $p$, raised to an arbitrary positive real power $\delta$.
Externí odkaz:
http://arxiv.org/abs/2011.10552