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pro vyhledávání: '"Britz, Thomas"'
In this paper, we present the harmonic generalizations of well-known polynomials of codes over finite fields, namely the higher weight enumerators and the extended weight enumerators, and we derive the correspondences between these weight enumerators
Externí odkaz:
http://arxiv.org/abs/2405.16948
The Ramsey numbers $R(T_n,W_8)$ are determined for each tree graph $T_n$ of order $n\geq 7$ and maximum degree $\Delta(T_n)$ equal to either $n-4$ or $n-5$. These numbers indicate strong support for the conjecture, due to Chen, Zhang and Zhang and to
Externí odkaz:
http://arxiv.org/abs/2403.02593
In this note, we give direct constructions of some group divisible designs (GDDs) with block size $4$ that have up to $50$ points.
Comment: arXiv admin note: text overlap with arXiv:2309.12823
Comment: arXiv admin note: text overlap with arXiv:2309.12823
Externí odkaz:
http://arxiv.org/abs/2401.11809
In this paper, we consider the existence of group divisible designs (GDDs) with block size $4$ and group sizes $4$ and $7$. We show that there exists a 4-GDD of type $4^t 7^s$ for all but a finite specified set of feasible values for $(t, s)$.
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Externí odkaz:
http://arxiv.org/abs/2309.12823
Autor:
Britz, Thomas, Chakraborty, Himadri Shekhar, Ishikawa, Reina, Miezaki, Tsuyoshi, Tang, Hopein Christofen
In this work, we introduce the harmonic generalization of the $m$-tuple weight enumerators of codes over finite Frobenius rings. A harmonic version of the MacWilliams-type identity for $m$-tuple weight enumerators of codes over finite Frobenius ring
Externí odkaz:
http://arxiv.org/abs/2210.16490
We present new values and bounds on the (normalised) closeness centrality $\bar{\mathsf{C}}_C$ of connected graphs and on its product $\bar{l}\bar{\mathsf{C}}_C$ with the mean distance $\bar{l}$ of these graphs. Our main result presents the fundament
Externí odkaz:
http://arxiv.org/abs/2204.11283
Publikováno v:
In Discrete Mathematics February 2025 348(2)
Autor:
Li, Nero Ziyu, Britz, Thomas
Extending previous results in the literature, random colored substitution networks and degree dimension are defined in this paper. The scale-freeness of these networks is proved by introducing a new definition for degree dimension that is associated
Externí odkaz:
http://arxiv.org/abs/2109.14463
In this paper we provide a $4$-GDD of type $2^2 5^5$, thereby solving the existence question for the last remaining feasible type for a $4$-GDD with no more than $30$ points. We then show that $4$-GDDs of type $2^t 5^s$ exist for all but a finite spe
Externí odkaz:
http://arxiv.org/abs/2109.11221
For trace class operators $A, B \in \mathcal{B}_1(\mathcal{H})$ ($\mathcal{H}$ a complex, separable Hilbert space), the product formula for Fredholm determinants holds in the familiar form \[ {\det}_{\mathcal{H}} ((I_{\mathcal{H}} - A) (I_{\mathcal{H
Externí odkaz:
http://arxiv.org/abs/2007.12834