8 papers
Proposal of a generating function of partition sequences
Masanori Ando
In this paper, we introduce the generating functions of partition sequences. Partition sequences have a one-to-one correspondence with partitions. Therefore, the generating functio…
Generalizations of Sylvester's refinement of Euler's odd-strict theorem
Masanori Ando
Regarding Euler's odd-strict theorem, which is the most basic partition identity, A refinement was done by Sylvester, and it was generalized by Bessenrodt to the r-regular and r-cl…
The Baumkuchen Theorem
Masanori Ando, Tadayuki Haraguchi
In this paper, we present the Baumkuchen Theorem related to the combination of divided Baumkuchen pieces. It can be proved using the basic properties of elementary geometry. We als…
A combinatorial proof of the supper symmetric property of hook length
Masanori Ando
There are kinds of length hooks with different arm length. Actually, this kinds appear uniformly in Young diagrams of size . The property ``appear uniformly'' is cal…
Inferior Regular Partitions and Glaisher Correspondence
Masanori Ando
In this paper, we proof Mizukawa-Yamada's and -tuple version of this.
Odd number and Trapezoidal number
Masanori Ando
In this paper, we give a bijective proof of the reduced lecture hall partition theorem. It is possible to extend this bijection in lecture hall partition theorem. And refined versi…
A combinatorial proof of an identity for the divisor generating function
Masanori Ando
We translate Uchimura's identity for the divisor function and whose generalizations into combinatorics of partitions, and give a combinatorial proof of them. As a by-product of the…
Combinatorics for graded Cartan matrices of the Iwahori-Hecke algebra of type A
Masanori Ando, Takeshi Suzuki, Hiro-Fumi Yamada
A -analogue of combinatorics concerning the Cartan matrix for the Iwahori-Hecke algebra of type is investigated. We give several descriptions for the determinant of the grad…