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We construct a ternary [49,25,7] code from the row span of a Jacobsthal matrix. It is equivalent to a Generalized Quadratic Residue (GQR) code in the sense of van Lint and MacWilliams (1978). These codes are the abelian generalizations of the quadrat
Externí odkaz:
http://arxiv.org/abs/2407.16310
Autor:
Xin, Guoce, Zhang, Chen
The Sylvester's denumerant \( d(t; \boldsymbol{a}) \) is a quantity that counts the number of nonnegative integer solutions to the equation \( \sum_{i=1}^{N} a_i x_i = t \), where \( \boldsymbol{a} = (a_1, \dots, a_N) \) is a sequence of distinct pos
Externí odkaz:
http://arxiv.org/abs/2406.18975
In this paper, we focus on knapsack cones, a specific type of simplicial cones that arise naturally in the context of the knapsack problem $x_1 a_1 + \cdots + x_n a_n = a_0$. We present a novel combinatorial decomposition for these cones, named \text
Externí odkaz:
http://arxiv.org/abs/2406.13974
Autor:
Gibbs, Amelia, Miceli, Brian K.
The main goal of this paper is to assign two combinatorial interpretations to the elements of the Rascal Triangle defined by Angorro et al. The first interpretation involves counting ascents in binary words, while the second interpretation involves p
Externí odkaz:
http://arxiv.org/abs/2405.11045
Autor:
Makowsky, Johann A.
In this paper I survey the sources of inspiration for my own and co-authored work in trying to develop a general theory of graph polynomials. I concentrate on meta-theorems, i.e., theorem which depend only on the form infinite classes of graph polyno
Externí odkaz:
http://arxiv.org/abs/2405.02617
Autor:
Bajnok, Bela
Publikováno v:
Graphs and Combinatorics, v. 14, (1998), pp. 97-107
Spherical t-designs are Chebyshev-type averaging sets on the d-sphere S^d which are exact for polynomials of degree at most t. This concept was introduced in 1977 by Delsarte, Goethals, and Seidel, who also found the minimum possible size of such des
Externí odkaz:
http://arxiv.org/abs/2404.15544
Autor:
Chaudhary, Vivek
Graph coloring is a problem with varied applications in industry and science such as scheduling, resource allocation, and circuit design. The purpose of this paper is to establish if a new gradient based iterative solver framework known as heat diffu
Externí odkaz:
http://arxiv.org/abs/2404.14457
Autor:
Meng, Ruoyu, Ramamoorthy, Aditya
We consider the problem of zero-error function computation with side information. Alice has a source $X$ and Bob has correlated source $Y$ and they can communicate via either classical or a quantum channel. Bob wants to calculate $f(X,Y)$ with zero e
Externí odkaz:
http://arxiv.org/abs/2402.01549
Autor:
G, Dhawlath., V, Raja.
The power graph of a group $G$, denoted as $P(G)$, constitutes a simple undirected graph characterized by its vertex set $G$. Specifically, vertices $a,b$ exhibit adjacency exclusively if $a$ belongs to the cyclic subgroup generated by $b$ or vice ve
Externí odkaz:
http://arxiv.org/abs/2401.11873
Autor:
Li, An-Ping
In this paper, we will continue the investigation of Waring's problem, and give further improvements.
Comment: An update of the data in the last paragraph with a modification
Comment: An update of the data in the last paragraph with a modification
Externí odkaz:
http://arxiv.org/abs/2401.13436