20 citations · 169 across the 56 of their papers we have counts for
10 papers · 1 filter
-numerical semigroups of Pell triples
Takao Komatsu, Jiaxin Mu
For a nonnegative integer , the -numerical semigroup is defined as the set of integers whose nonnegative integral linear combinations of given positive integers $a_1,a_…
Analytic aspects of -analogue of poly-Stirling numbers of both kinds
Takao Komatsu, Eli Bagno, David Garber
The Stirling numbers of type of the second kind count signed set partitions. In this paper we provide new combinatorial and analytical identities regarding these numbers as wel…
-numerical semigroups with -symmetric properties
Takao Komatsu, Haotian Ying
The so-called Frobenius number in the famous linear Diophantine problem of Frobenius is the largest integer such that the linear equation ($a_1,\dots,a_k…
The -Frobenius and -Sylvester numbers for Fibonacci and Lucas triplets
Takao Komatsu, Haotian Ying
In this paper we study a certain kind of generalized linear Diophantine problem of Frobenius. Let be positive integers such that their greatest common divisor i…
Asymmetric Circular Graph with Hosoya Index and Negative Continued Fractions
Takao Komatsu
It has been known that the Hosoya index of caterpillar graph can be calculated as the numerator of the simple continued fraction. Recently, the author \cite{Komatsu2020} introduces…
Continued fractions associated with the topological index of the caterpillar-bond graph
Takao Komatsu
In this paper, we give graphs whose topological index are exactly equal to the number , satisfying the three term recurrence relation $$ u_n=a u_{n-1}+b u_{n-2}\quad(n\ge 2)\q…