T. Komatsu

activity

20032023

most citedThe Frobenius number for sequences of triangular numbers associated with number of solutions

20 citations · 169 across the 56 of their papers we have counts for

collaborators

56 papers

math.CO2023★ 3 cited

$p$ -numerical semigroups of Pell triples

Takao Komatsu, Jiaxin Mu

For a nonnegative integer $p$ , the $p$ -numerical semigroup $S_{p}$ is defined as the set of integers whose nonnegative integral linear combinations of given positive integers $a_1,a_…

math.NT2023

$p$ -numerical semigroup of generalized Fibonacci triples

Takao Komatsu, Shanta Laishram, Pooja Punyani

For a nonnegative integer $p$ , we give explicit formulas for the $p$ -Frobenius number and the $p$ -genus of generalized Fibonacci numerical semigroups. Here, the $p$ -numerical semig…

math.NT2022★ 3 cited

Sylvester sums on the Frobenius set in arithmetic progression with initial gaps

Takao Komatsu

Let $a_{1}, a_{2}, \dots, a_{k}$ be positive integers with $g cd (a_{1}, a_{2}, \dots, a_{k}) = 1$ . Frobenius number is the largest positive integer that is NOT representable in terms of $a_1,a_2,\dots…

math.NT2022

The Frobenius number for shifted geometric sequences associated with the number of solutions

Takao Komatsu

For a non-negative integer $p$ , one of the generalized Frobenius numbers, that is called the $p$ -Frobenius number, is the largest integer that is represented at most in $p$ ways as…

math.CO2022★ 1 cited

Analytic aspects of $q, r$ -analogue of poly-Stirling numbers of both kinds

Takao Komatsu, Eli Bagno, David Garber

The Stirling numbers of type $B$ of the second kind count signed set partitions. In this paper we provide new combinatorial and analytical identities regarding these numbers as wel…

math.CO2022

$p$ -numerical semigroups with $p$ -symmetric properties

Takao Komatsu, Haotian Ying

The so-called Frobenius number in the famous linear Diophantine problem of Frobenius is the largest integer such that the linear equation $a_{1} x_{1} + \dots + a_{k} x_{k} = n$ ($a_1,\dots,a_k…

p-numerical semigroups of Pell triples

p-numerical semigroup of generalized Fibonacci triples