Russelle Guadalupe

activity

20212026

most citedA note on the exact formulas for certain

2

-color partitions

3 citations · 9 across the 18 of their papers we have counts for

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18 papers · 1 filter

math.NT2026

Congruences modulo powers of $2$ for three restricted partition functions of Pushpa and Vasuki

Russelle Guadalupe

We establish infinite families of congruences modulo arbitrary powers of $2$ for the three restricted partition functions $M (n), T^{*} (n)$ , and $P^{*} (n)$ introduced by Pushpa an…

math.NT2026

Linear identities for partition pairs with $5$ -cores

Russelle Guadalupe

We prove an infinite family of linear identities for the number $A_{5} (n)$ of partition pairs of $n$ with $5$ -cores by using certain theta function identities involving the Ramanujan…

math.NT2026

Linear identities for partition pairs with 4-cores

Russelle Guadalupe

We determine an infinite family of linear identities for the number $A_{4} (n)$ of partition pairs of $n$ with $4$ -cores by employing elementary $q$ -series techniques and certain $3$ -…

math.NT2025

Congruences for an analogue of Lin's partition function

Russelle Guadalupe

We study certain arithmetic properties of an analogue $B (n)$ of Lin's restricted partition function that counts the number of partition triples $π = (π_{1}, π_{2}, π_{3})$ of $n$ such that $…

math.NT2025

A note on congruences modulo 7 and 11 for two restricted partition functions

Russelle Guadalupe

For an integer $c \geq 1$ , let $a_{c} (n)$ count the number of generalized cubic partitions of $n$ , which are partitions of $n$ whose even parts may appear in $c$ different colors, and…

math.NT2025★ 3 cited

A note on congruences for the difference between even cranks and odd cranks

Russelle Guadalupe

Recently, Amdeberhan and Merca proved some arithmetic properties of the crank parity function $C (n)$ defined as the difference between the number of partitions of $n$ with even cra…

math.NT2025

The $k$ -elongated plane partition function modulo small powers of $5$

Russelle Guadalupe

Andrews and Paule revisited combinatorial structures known as the $k$ -elongated partition diamonds, which were introduced in connection with the study of the broken $k$ -diamond par…

math.NT2025

Remarks on a certain restricted partition function of Lin

Russelle Guadalupe

Let $b (n)$ be the number of partition triples $π = (π_{1}, π_{2}, π_{3})$ of $n$ such that $π_{1}$ consists of distinct odd parts, and $π_{2}$ and $π_{3}$ consist of parts divisible by $4$ . Utiliz…

math.NT2025

New Gosper-type Lambert series identities of levels 12 and 16

Russelle Guadalupe

We derive new Gosper-type Lambert series identities of levels $12$ and $16$ using certain sums of generalized $η$ -quotients on the genus zero congruence subgroups $Γ_{0} (12)$ and $Γ_…

math.NT2024

Gosper-type Lambert series identities of level 14

Russelle Guadalupe

We derive two Gosper-type Lambert series identities of level $14$ which involve the $q$ -constant $Π_{q}$ using a special case of Bailey's $_{6} ψ_{6}$ summation formula and certain propet…

math.NT2024

A remark on modular equations involving Rogers-Ramanujan continued fraction via $5$ -dissections

Russelle Guadalupe

In this paper, we study the $5$ -dissections of certain Ramanujan's theta functions, particularly $ψ (q) ψ (q^{2}), φ (- q)$ and $φ (- q) φ (- q^{2})$ , and derive an identity for $q(q;q)_{\infty}…

math.NT2024

A note on congruences for generalized cubic partitions modulo primes

Russelle Guadalupe

Recently, Amdeberhan, Sellers, and Singh introduced the notion of a generalized cubic partition function $a_{c} (n)$ and proved two isolated congruences via modular forms, namely, $a_…

math.NT2024

Modularity of certain products of the Rogers-Ramanujan continued fraction

Russelle Guadalupe

We study the modularity of the functions of the form $r (τ)^{a} r (2 τ)^{b}$ , where $a$ and $b$ are integers with $(a, b) \neq = (0, 0)$ and $r (τ)$ is the Rogers-Ramanujan continued fraction, w…

math.NT2024★ 2 cited

Ramanujan's continued fractions of order $10$ as modular functions

Victor Manuel Aricheta, Russelle Guadalupe

We explore the modularity of the continued fractions $I (τ), J (τ), T_{1} (τ), T_{2} (τ)$ and $U (τ) = I (τ) / J (τ)$ of order $10$ , where $I (τ)$ and $J (τ)$ are introduced by Rajkhowa and Saikia,…

math.NT2023

Some congruences for $3$ -core cubic bipartitions

Russelle Guadalupe

In this paper, we derive certain congruences for the number of $3$ -core cubic bipartitions using elementary $q$ -series manipulations and dissection formulas.

math.NT2023★ 1 cited

Analogue of Ramanujan's function $k (τ)$ for the continued fraction $X (τ)$ of order six

Russelle Guadalupe, Victor Manuel Aricheta

Motivated by the recent work of Park on the analogue of the Ramanujan's function $k (τ) = r (τ) r^{2} (2 τ)$ for the Ramanujan's cubic continued fraction, where $r (τ)$ is the Rogers-Ramanuj…

math.NT2022

A note on the squares of the form $\prod_{k = 1}^{n} (2 k^{2} + l)$ with $l$ odd

Russelle Guadalupe

Let $l$ be a positive odd integer. Using Cilleruelo's method, we establish an explicit lower bound $N_{l}$ depending on $l$ such that for all $n \geq N_{l}$ , $\prod_{k = 1}^{n} (2 k^{2} + l)$ is…

math.NT2021

On the $3$ -adic valuation of the Narayana numbers

Russelle Guadalupe

We define the Narayana sequence ${a_{n}}_{n \geq 0}$ as the one satisfying the linear recurrence relation $a_{n} = a_{n - 1} + a_{n - 3}$ for $n \geq 3$ , with initial values $a_{0} = 0$ and $a…

Congruences modulo powers of 2 for three restricted partition functions of Pushpa and Vasuki

Linear identities for partition pairs with 5-cores

Linear identities for partition pairs with 4-cores

Congruences for an analogue of Lin's partition function

A note on congruences modulo 7 and 11 for two restricted partition functions

A note on congruences for the difference between even cranks and odd cranks

The k-elongated plane partition function modulo small powers of 5

Remarks on a certain restricted partition function of Lin

New Gosper-type Lambert series identities of levels 12 and 16

Gosper-type Lambert series identities of level 14

A remark on modular equations involving Rogers-Ramanujan continued fraction via 5-dissections

A note on congruences for generalized cubic partitions modulo primes

Modularity of certain products of the Rogers-Ramanujan continued fraction

Ramanujan's continued fractions of order 10 as modular functions

Some congruences for 3-core cubic bipartitions

Analogue of Ramanujan's function k(τ) for the continued fraction X(τ) of order six

A note on the squares of the form ∏k=1n​(2k2+l) with l odd

On the 3-adic valuation of the Narayana numbers

Congruences modulo powers of $2$ for three restricted partition functions of Pushpa and Vasuki

Linear identities for partition pairs with $5$ -cores

The $k$ -elongated plane partition function modulo small powers of $5$

A remark on modular equations involving Rogers-Ramanujan continued fraction via $5$ -dissections

Ramanujan's continued fractions of order $10$ as modular functions

Some congruences for $3$ -core cubic bipartitions

Analogue of Ramanujan's function $k (τ)$ for the continued fraction $X (τ)$ of order six

A note on the squares of the form $\prod_{k = 1}^{n} (2 k^{2} + l)$ with $l$ odd

On the $3$ -adic valuation of the Narayana numbers