Zobrazeno 1 - 10
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pro vyhledávání: '"Riordan, P"'
Autor:
Frankson, Shakuan
The Riordan group is a set of infinite lower-triangular matrices defined by two generating functions, $g$ and $f$. The elements of the group are called Riordan arrays, denoted by $(g,f)$, and the $k$th column of a Riordan array is given by the functi
Externí odkaz:
http://arxiv.org/abs/2410.10709
Autor:
He, Tian-Xiao
In this paper, we define double almost-Riordan arrays and find that the set of all double almost-Riordan arrays forms a group, called the double almost-Riordan group. We also obtain the sequence characteristics of double almost-Riordan arrays and giv
Externí odkaz:
http://arxiv.org/abs/2411.05334
Autor:
Barry, Paul
We study a family of Riordan arrays whose square symmetrizations lead to the Robbins numbers as well as numbers associated to the $20$ vertex model. We provide closed-form expressions for the elements of these arrays, and also give a canonical Catala
Externí odkaz:
http://arxiv.org/abs/2409.09547
Autor:
Krylov, Nikolai A.
When $p(t)$ is a polynomial of degree $d$, $k$-th column of the Riordan array $\bigl(1/(1 - t^{d+1}), tp(t)\bigr)$ is an eventually periodic sequence with the repeating part beginning at the $1 + (k-1)(d+1)$-st term. The pre-periodic terms add up to
Externí odkaz:
http://arxiv.org/abs/2407.19530
Autor:
He, Tian-Xiao, Słowik, Roksana
In this paper the total positivity of quasi-Riordan arrays is investigated with use of the sequence characterization of quasi-Riordan arrays. Due to the correlation between quasi-Riordan arrays and Riordan arrays, this study is an in-depth discussion
Externí odkaz:
http://arxiv.org/abs/2406.07120
Autor:
He, Tian-Xiao, Słowik, Roksana
In this paper we study the total positivity of almost-Riordan arrays $(d(t)|\, g(t), f(t))$ and establish its necessary conditions and sufficient conditions, particularly, for some well used formal power series $d(t)$. We present a semidirect product
Externí odkaz:
http://arxiv.org/abs/2406.03774
Autor:
He, Tian-Xiao, Krylov, Nikolai A.
We prove that a Coxeter group containing an element of finite order, which is generated by two non-commuting involutions, can not be embedded into the Riordan group.
Comment: 13 pages
Comment: 13 pages
Externí odkaz:
http://arxiv.org/abs/2405.10470
Publikováno v:
Demonstratio Mathematica, Vol 57, Iss 1, Pp 205-214 (2024)
In this article, we define three-dimensional q-Riordan arrays and q-Riordan representations for these arrays. Also, we give four cases of infinite multiplication three-dimensional matrices of these arrays. As applications, we obtain three-dimensional
Externí odkaz:
https://doaj.org/article/3cb22564a8654676b5907d46e96ec2dc
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