논문KCI 등재
Arithmetic properties of triangular partitions
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초록
We obtain a two variable generating function for the number of triangular partitions. Using this generating function, we study arithmetic properties of a certain weighted count of triangular partitions. Finally, we introduce a rank-type function for triangular partitions, which gives a combinatorial explanation for a triangular partition congruence.
Abstract
We obtain a two variable generating function for the number of triangular partitions. Using this generating function, we study arithmetic properties of a certain weighted count of triangular partitions. Finally, we introduce a rank-type function for triangular partitions, which gives a combinatorial explanation for a triangular partition congruence.
참고문헌 (8)
- G.E. Andrews, "The Theory of Partitions" (1998), Cambridge University Press
- G.E. Andrews, "Dyson’s crank of a partition", Bull. Amer. Math. Soc., 18(2), pp.167~171 (1988)
- A. O. L. Atkin, "Some properties of partitions", Proc. London Math. Soc, 4, pp.84~106 (1954)
- B.C. Berndt, "Number theory in the spirit of Ramanujan", Student Mathematical Library, 34 (2006), American Mathematical Society
- F. J. Dyson, "Some guesses in the theory of partitions", Eureka, 8, pp.10~15 (1944)
- F. Garvan, "New combinatorial interpretations of Ramanujan’s partition congruences mod 5, 7 and 11", Trans. Amer. Math. Soc., 305(1), pp.47~77 (1988)
- B. Kim, "Group Actions on Partitions", Elect. J. Comb, 24 (2017)
- 김병찬, "Polygonal partitions", 한국수학논문집, 26(2), pp.167~174 (2018), 강원경기수학회
관련 논문AI추천
Congruences modulo 7 and 11 for (s,t)-regular bipartitionsRanganatha D.장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2018 · 제21권 제2호Cubic partition pairs weighted by the parity of the crank김병찬강원경기수학회 · 한국수학논문집2015 · 제23권 제4호Arithmetic properties of partition four tuples with 3-coresChandrashekar Adiga, Ranganatha D장전수학회 · Advanced Studies in Contemporary Mathematics2016 · 제26권 제3호Polygonal partitions김병찬강원경기수학회 · 한국수학논문집2018 · 제26권 제2호Some Congruence Properties for Ramanujan’s General PartitionsB. R. S. Kumar, D. A. Radha, Shruthi Hegde장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2020 · 제23권 제3호Further results on biases in integer partitionsShane Chern대한수학회 · 대한수학회보2022 · 제59권 제1호
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