On $3^k$-regular cubic partitions

Nayandeep Deka Baruah; Hirakjyoti Das

doi:10.4134/JKMS.j210517

논문KCI 등재

On $3^k$-regular cubic partitions

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

Congruence $m$-regular cubic partition

주제분류수학

초록

Recently, Gireesh, Shivashankar, and Naika \cite{GSN20} found some infinite classes of congruences for the 3- and the 9-regular cubic partitions modulo powers of 3. We extend their study to all the $3^k$-regular cubic partitions. We also find new families of congruences.

Abstract

Recently, Gireesh, Shivashankar, and Naika \cite{GSN20} found some infinite classes of congruences for the 3- and the 9-regular cubic partitions modulo powers of 3. We extend their study to all the $3^k$-regular cubic partitions. We also find new families of congruences.

참고문헌 (21)

Z. Ahmed, "New congruences for ℓ-regular partitions for ℓ ∈ {5, 6, 7, 49}", Ramanujan J, 40(3), pp.649~668 (2016)[DOI]
N. D. Baruah, "Generating functions and congruences for 9-regular and 27-regular partitions in 3 colours", Hardy-Ramanujan J, 44, pp.101~115 (2021)
N. D. Baruah, "Infinite families of arithmetic identities and congruences for bipartitions with 3-cores", J. Number Theory, 149, pp.92~104 (2015)[DOI]
B. C. Berndt, "Ramanujan’s notebooks. Part III" (1991), Springer-Verlag
R. Carlson, "Infinite families of infinite families of congruences for k-regular partitions", Ramanujan J, 33(3), pp.329~337 (2014)[DOI]
H. -C. Chan, "Ramanujan’s cubic continued fraction and an analog of his “most beautiful identity”", Int. J. Number Theory, 6(3), pp.673~680 (2010)[DOI]
H. -C. Chan, "Ramanujan’s cubic continued fraction and Ramanujan type congruences for a certain partition function", Int. J. Number Theory, 6(4), pp.819~834 (2010)[DOI]
H. -C. Chan, "Distribution of a certain partition function modulo powers of primes", Acta Math. Sin. (Engl. Ser.), 27(4), pp.625~634 (2011)[DOI]
H. H. Chan, "New analogues of Ramanujan’s partition identities", J. Num-ber Theory, 130(9), pp.1898~1913 (2010)[DOI]
B. Dandurand, "ℓ-divisibility of ℓ-regular partition functions", Ramanu-jan J, 19(1), pp.63~70 (2009)[DOI]
D. S. Gireesh, "On 3- and 9-regular cubic partitions", J. Integer Seq, 23(7), pp.12~ (2020)
M. D. Hirschhorn, "Cubic partitions modulo powers of 5", Ramanujan J, 51(1), pp.67~84 (2020)[DOI]
M. Hirschhorn, "Cubic analogues of the Jacobian theta func-tion θ(z, q)", Canad. J. Math, 45(4), pp.673~694 (1993)[DOI]
Q.-H. Hou, "Quadratic forms and congruences for ℓ-regular partitions modulo 3, 5 and 7", Adv. in Appl. Math, 70, pp.32~44 (2015)[DOI]
B. L. S. Lin, "Arithmetic of the 7-regular bipartition function modulo 3", Ramanujan J, 37(3), pp.469~478 (2015)[DOI]
S. Ramanujan, "Congruence properties of partitions", Proc. London Math. Soc, 18, pp.19~ (1920)
S. Ramanujan, "Congruence properties of partitions", Math. Z, 19(1–2), pp.147~153 (1921)
S. Ramanujan, "The lost notebook and other unpublished papers" (1988), Narosa
S. Ramanujan, "Some properties of p(n), the number of partitions of n", Proc. Cambridge Philos. Soc, 19, pp.207~210 (1919)
J. J. Webb, "Arithmetic of the 13-regular partition function modulo 3", Ramanujan J, 25(1), pp.49~56 (2011)[DOI]
X. Xiong, "The number of cubic partitions modulo powers of 5", Sci. Sin. Math, 41(1), pp.1~15 (2011)

이 간행물의 다른 논문 (9건)

The moduli spaces of Lorentzian left-invariant metrics on three-dimensional unimodular simply connected Lie groupsMohamed Boucetta, Abdelmounaim Chakkarpp. 651-684 Foliations from left ordersChenxi Wu, 백형렬, Sebastian Henselpp. 699-715 Uniqueness of quasi-roots in right-angled Artin groups이언경, 이상진pp. 717-731 Gorenstein quasi-resolving subcategoriesWeiqing Cao, Jiaqun Weipp. 733-756 Sharp Ore-type conditions for the existence of an even $[4,b]$-factor in a graph조은경, 오수일, 권수아pp. 757-774

키워드

초록

Abstract

참고문헌 (21)

관련 논문AI추천

이 간행물의 다른 논문 (9건)