Zobrazeno 1 - 10
of 125 908
pro vyhledávání: '"MATHEMATICS / Combinatorics"'
Let $W$ be a finite group generated by reflections of a lattice $M$. If a lattice polytope $P \subset M \otimes_{\mathbb Z}\mathbb R$ is preserved by $W$, then we show that the quotient of the projective toric variety $X_P$ by $W$ is isomorphic to th
Externí odkaz:
http://arxiv.org/abs/2410.14653
Autor:
Pham, Huy Tuan, Zakharov, Dmitrii
A set of integers $A$ is non-averaging if there is no element $a$ in $A$ which can be written as an average of a subset of $A$ not containing $a$. We show that the largest non-averaging subset of $\{1, \ldots, n\}$ has size $n^{1/4+o(1)}$, thus solvi
Externí odkaz:
http://arxiv.org/abs/2410.14624
Autor:
De Loera, Javier
For cluster algebras of surface type, Musiker, Schiffler and Williams gave a formula for cluster variables in terms of perfect matchings of snake graphs. Building on this, we provide a simple determinantal formula for cluster variables via the weight
Externí odkaz:
http://arxiv.org/abs/2410.14554
Autor:
Cobeli, Cristian, Zaharescu, Alexandru
For any odd prime $p$ and any integer $N\ge 0$, let $\mathcal{V}(p,N)$ be the set of vertices of the cyclotomic box $\mathscr{B} = \mathscr{B}(p,N)$ of edge size $2N$ and centered at the origin $O$ of the ring of integers $\mathbb{Z}[\omega]$ of the
Externí odkaz:
http://arxiv.org/abs/2410.14473
We study Hamiltonicity in the union of an $n$-vertex graph $H$ with high minimum degree and a binomial random graph on the same vertex set. In particular, we consider the case when $H$ has minimum degree close to $n/2$. We determine the perturbed thr
Externí odkaz:
http://arxiv.org/abs/2410.14447
We characterise partition regularity and density regularity for linear equations over the Piatetski-Shapiro numbers $\lfloor n^c \rfloor$ when $1 < c < (2s+6)/(s+8)$, where $s \geqslant 3$ is the number of variables.
Comment: 17 pages
Comment: 17 pages
Externí odkaz:
http://arxiv.org/abs/2410.14427
Motivated by a repair problem for fractional repetition codes in distributed storage, each block of any Steiner quadruple system (SQS) of order $v$ is partitioned into two pairs. Each pair in such a partition is called a nested design pair and its mu
Externí odkaz:
http://arxiv.org/abs/2410.14417
Autor:
Coron, Basile
Motivated by the question of whether Chow polynomials of matroids have only real roots, this article revisits the known relationship between Eulerian polynomials and the Hilbert series of Chow rings of permutohedral varieties. This is done using a qu
Externí odkaz:
http://arxiv.org/abs/2410.14199
Autor:
Guadalupe, Russelle
In this paper, we study the $5$-dissections of certain Ramanujan's theta functions, particularly $\psi(q)\psi(q^2), \varphi(-q)$ and $\varphi(-q)\varphi(-q^2)$, and derive an identity for $q(q;q)_{\infty}^6/(q^5;q^5)_{\infty}^6$ in terms of certain p
Externí odkaz:
http://arxiv.org/abs/2410.14149
Autor:
Chen, Dandan, Zou, Ziyin
Recently Andrews and Bachraoui proved identities relating certain restricted partitions into distinct even parts with restricted 4-regular partitions by the theory of basic hypergeometric series. They also posed a question regarding combinatorial pro
Externí odkaz:
http://arxiv.org/abs/2410.14126