arXiv subjects

Siyu Yin

Publications and source records attributed to Siyu Yin.

7 recordsLinked to original sources

arXiv2025

Congruences modulo powers of $3$ for generalized Frobenius partitions $C\Psi_{6,0}$

In 1984, Andrews introduced the family of partition functions $c\phi_k(n)$, which counts the number of generalized Frobenius partitions of $n$ with $k$ colors. In previous work, we proved a conjecture on congruences for $c\phi_6(n)$ modulo powers of 3. In this paper, we consider the $(6,0)$-colored Frobenius partition functions $c\psi_{6,0}(n)$. We establish a connection between the generating functions of $c\psi_{6,3}(n)$ and $c\psi_{6,0}(n)$ via an Atkin-Lehner involution, and prove congruences modulo powers of 3 for $c\psi_{6,0}(n)$.

math.CO↗

arXiv2025

Congruences modulo powers of $7$ for $k$-elongated plane partitions

The enumeration $d_k(n)$ of $k$-elongated plane partition diamonds has emerged as a generalization of the classical integer partition function $p(n)$. Congruences for $d_k(n)$ modulo certain powers of primes have been proven via elementary means and modular forms by many authors. Recently, Banerjee and Smoot established an infinite family of congruences for $d_5(n)$ modulo powers of 5. In this paper we have discovered an infinite congruence family for $d_3(n)$ and $d_5(n)$ modulo powers of 7.

math.NT↗

arXiv2025

Congruences modulo powers of $3$ for $6$-colored generalized Frobenius partitions

In $1984$, Andrews introduced the family of partition functions $c\phi_k(n)$, which enumerate generalized Frobenius partitions of $n$ with $k$ colors. In $2016$, Gu, Wang, and Xia established several congruences for $c\phi_6(n)$ and proposed a conjecture concerning congruences modulo powers of $3$ for this function. In this paper, we resolve a revised version of their conjecture by employing an approach analogous to that developed by Banerjee and Smoot.

math.CO↗

arXiv2024

A conjecture of Radu and Sellers on congruences modulo powers of 2 for broken 3-diamond partitions

In 2007, Andrews and Paule introduced the family of functions $\Delta_k(n)$, which enumerate the number of broken $k$-diamond partitions for a fixed positive integer $k$. In 2013, Radu and Sellers completely characterized the parity of $\Delta_3(8n+r)$ for certain values of $r$ and proposed a conjecture on congruences modulo powers of $2$ for broken $3$-diamond partitions. In this paper, we employ an unconventional $U$-sequence to resolve the revised conjecture put forward by Radu and Sellers.

math.CO↗

arXiv2024

Rogers-Ramanujan Type Identities Involving Double Sums

We prove four new Rogers-Ramanujan-type identities for double series. They follow from the classical Rogers-Ramanujan identities using the constant term method and properties of Rogers-Szegő polynomials.

math.NT↗

arXiv2024

A conjecture of Gasper on $q$-ultraspherical polynomials

In this paper we establish $q$-orthogonality relation for the continuous $q$-ultraspherical polynomials, which was considered by Gasper. Additionally, we evaluate a new $q$-beta integral with several parameters.

math.CA↗

arXiv2024

On the total number of ones associated with cranks of partitions modulo 11

In 2021, Andrews mentioned that George Beck introduced partition statistics $M_w(r,m,n)$, which denote the total number of ones in the partition of $n$ with crank congruent to $r$ modulo $m$. Recently, a number of congruences and identities involving $M_w(r,m,n)$ for some small $m$ have been developed. We establish the 11-dissection of the generating functions for $M_ω(r,11,n)-M_ω(11-r,11,n)$, where $r=1,2,3,4,5$. In particular, we discover a beautiful identity involving $M_ω(r,11,11n+6)$.

math.CO↗