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Masanori Ando

Publications and source records attributed to Masanori Ando.

8 recordsLinked to original sources
arXiv2025

Proposal of a generating function of partition sequences

In this paper, we introduce the generating functions of partition sequences. Partition sequences have a one-to-one correspondence with partitions. Therefore, the generating function has no multiplicity and appears meaningless initially. However, we show that using a matrix can give meaning to the coefficients and preserve valuable information about partitions. We also introduce some restrictions on partitions suitable for these generating functions.

math.CO↗
arXiv2023

Generalizations of Sylvester's refinement of Euler's odd-strict theorem

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-class regular cases. In this paper, we focus on the periodicity of the exponent seen on the r-regular side in Bessenrodt's generalization, and further generalize from that point of view. At the end of this paper, we also introduce a partition identity when extended without regard to the periodicity of the exponent.

math.CO↗
arXiv2020

The Baumkuchen Theorem

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 also apply some lemmas to prove the Pizza Theorem.

math.HO↗
arXiv2019

A combinatorial proof of the supper symmetric property of hook length

There are $k$ kinds of length $k$ hooks with different arm length. Actually, this $k$ kinds appear uniformly in Young diagrams of size $n$. The property ``appear uniformly'' is called super symmetric. We give a combinatorial proof of the supper symmetric property of hook length.

math.CO↗
arXiv2015

Odd number and Trapezoidal number

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 versions of each theorems are also presented.

math.CO↗
arXiv2012

Combinatorics for graded Cartan matrices of the Iwahori-Hecke algebra of type A

A $q$-analogue of combinatorics concerning the Cartan matrix for the Iwahori-Hecke algebra of type $A$ is investigated. We give several descriptions for the determinant of the graded Cartan matrix, which imply some combinatorial identities. A conjectural expression for the elementary divisors is also presented.

math.CO↗