Zobrazeno 1 - 10
of 48
pro vyhledávání: '"Schmitt, John R."'
In 1976 Martin Gardner posed the following problem: ``What is the smallest number of [queens] you can put on an [$n \times n$ chessboard] such that no [queen] can be added without creating three in a row, a column, or a diagonal?'' The work of Cooper
Externí odkaz:
http://arxiv.org/abs/2401.03119
Autor:
Caro, Yair, Schmitt, John R.
We generalize the notion of Erd\H{o}s-Ginzburg-Ziv constants -- along the same lines we generalized in earlier work the notion of Davenport constants -- to a ``higher degree" and obtain various lower and upper bounds. These bounds are sometimes exact
Externí odkaz:
http://arxiv.org/abs/2207.08682
Label the vertices of the complete graph $K_v$ with the integers $\{ 0, 1, \ldots, v-1 \}$ and define the length of the edge between $x$ and $y$ to be $\min( |x-y| , v - |x-y| )$. Let $L$ be a multiset of size $v-1$ with underlying set contained in $
Externí odkaz:
http://arxiv.org/abs/2105.00980
Publikováno v:
Integers 21 (2021), Paper No. A120, 17 pp
We generalize the notion of Davenport constants to a `higher degree' and obtain various lower and upper bounds, which are sometimes exact as is the case for certain finite commutative rings of prime power cardinality. Two simple examples that capture
Externí odkaz:
http://arxiv.org/abs/2102.06050
The conjecture, still widely open, posed by Marco Buratti, Peter Horak and Alex Rosa states that a list $L$ of $v-1$ positive integers not exceeding $\left\lfloor \frac{v}{2}\right\rfloor$ is the list of edge-lengths of a suitable Hamiltonian path of
Externí odkaz:
http://arxiv.org/abs/1912.07377
Let $(G,+)$ be an abelian group and consider a subset $A \subseteq G$ with $|A|=k$. Given an ordering $(a_1, \ldots, a_k)$ of the elements of $A$, define its {\em partial sums} by $s_0 = 0$ and $s_j = \sum_{i=1}^j a_i$ for $1 \leq j \leq k$. We consi
Externí odkaz:
http://arxiv.org/abs/1809.02684
Publikováno v:
In Discrete Mathematics September 2021 344(9)
A 1993 result of Alon and F\"uredi gives a sharp upper bound on the number of zeros of a multivariate polynomial over an integral domain in a finite grid, in terms of the degree of the polynomial. This result was recently generalized to polynomials o
Externí odkaz:
http://arxiv.org/abs/1508.06020
We present a restricted variable generalization of Warning's Second Theorem (a result giving a lower bound on the number of solutions of a low degree polynomial system over a finite field, assuming one solution exists). This is analogous to Brink's r
Externí odkaz:
http://arxiv.org/abs/1404.7793
Publikováno v:
The American Mathematical Monthly, 121:3 (March, 2014), pp. 213-221
In Martin Gardner's October, 1976 Mathematical Games column in Scientific American, he posed the following problem: "What is the smallest number of [queens] you can put on a board of side n such that no [queen] can be added without creating three in
Externí odkaz:
http://arxiv.org/abs/1206.5350