Zobrazeno 1 - 10
of 145
pro vyhledávání: '"Baruah, Nayandeep Deka"'
A partition is said to be $\ell$-regular if none of its parts is a multiple of $\ell$. Let $b^\prime_5(n)$ denote the number of 5-regular partitions into distinct parts (equivalently, into odd parts) of $n$. This function has also close connections t
Externí odkaz:
http://arxiv.org/abs/2411.02978
We prove some new modular identities for the Rogers\textendash Ramanujan continued fraction. For example, if $R(q)$ denotes the Rogers\textendash Ramanujan continued fraction, then \begin{align*}&R(q)R(q^4)=\dfrac{R(q^5)+R(q^{20})-R(q^5)R(q^{20})}{1+
Externí odkaz:
http://arxiv.org/abs/2410.17110
Publikováno v:
Journal of Integer Sequences 27 (2024), Article 24.4.5
Recently, Gireesh, Ray, and Shivashankar studied an analog, $\overline{a}_t(n)$, of the $t$-core partition function, $c_t(n)$. In this paper, we study the function $\overline{a}_5(n)$ in conjunction with $c_5(n)$ as well as another analogous function
Externí odkaz:
http://arxiv.org/abs/2409.02034
Publikováno v:
Integers 23 (2023), A40
Recently, Jha (arXiv:2007.04243, arXiv:2011.11038) has found identities that connect certain sums over the divisors of $n$ to the number of representations of $n$ as a sum of squares and triangular numbers. In this note, we state a generalized result
Externí odkaz:
http://arxiv.org/abs/2409.02023
Publikováno v:
Integers 21 (2021), A83
Recently, Merca and Schmidt found some decompositions for the partition function $p(n)$ in terms of the classical M\"{o}bius function as well as Euler's totient. In this paper, we define a counting function $T_k^r(m)$ on the set of $n$-color partitio
Externí odkaz:
http://arxiv.org/abs/2409.02004
Partitions wherein the even parts appear in two different colours are known as cubic partitions. Recently, Merca introduced and studied the function $A(n)$, which is defined as the difference between the number of cubic partitions of $n$ into an even
Externí odkaz:
http://arxiv.org/abs/2301.10501
For the unrestricted partition function $p(n)$ for integers $n \geq 0$, it is known that $p(49n + 19) \equiv 0 \pmod{49}$, $p(49n + 33) \equiv 0 \pmod{49}$, and $p(49n + 40) \equiv 0 \pmod{49}$ for all $n \geq 0$. We find witness identities for these
Externí odkaz:
http://arxiv.org/abs/2207.10697
In the eleventh paper in the series on MacMahons partition analysis, Andrews and Paule [1] introduced the $k$ elongated partition diamonds. Recently, they [2] revisited the topic. Let $d_k(n)$ count the partitions obtained by adding the links of the
Externí odkaz:
http://arxiv.org/abs/2207.06264
Publikováno v:
The Ramanujan Journal, Vol. 59, Issue 2, pp. 511--548, 2022
We show that the series expansions of certain $q$-products have \textit{matching coefficients} with their reciprocals. Several of the results are associated to Ramanujan's continued fractions. For example, let $R(q)$ denote the Rogers-Ramanujan conti
Externí odkaz:
http://arxiv.org/abs/2110.15546
Publikováno v:
Research in Number Theory, 2021
Recently, Chan and Wang (Fractional powers of the generating function for the partition function. Acta Arith. 187(1), 59--80 (2019)) studied the fractional powers of the generating function for the partition function and found several congruences sat
Externí odkaz:
http://arxiv.org/abs/2006.07811