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pro vyhledávání: '"05A99"'
$n$-circuits are series-parallel networks composed of exactly $n$ unit resistors. This paper is focused on evaluating the mean resistance of all $n$-circuits, $M_n$, establishing that it lies between $1$ and $4.3954$ for all $n$. We ultimately conjec
Externí odkaz:
http://arxiv.org/abs/2410.07261
Autor:
Kaul, Hemanshu, Mudrock, Jeffrey A.
The classic enumerative functions for counting colorings of a graph $G$, such as the chromatic polynomial $P(G,k)$, do so under the assumption that the given graph is labeled. In 1985, Hanlon defined and studied the chromatic polynomial for an unlabe
Externí odkaz:
http://arxiv.org/abs/2409.06063
Autor:
Ferrari, Luca, Verciani, Francesco
Naples parking functions were introduced as a generalization of classical parking functions, in which cars are allowed to park backwards, by checking up to a fixed number of previous spots, before proceeding forward as usual. In this work we introduc
Externí odkaz:
http://arxiv.org/abs/2405.07522
The amplituhedron $A_{n,k,m}$ is a geometric object introduced in the context of scattering amplitudes in $N=4$ super Yang Mills. It generalizes the positive Grassmannian (when $n=k+m$), cyclic polytopes (when $k=1$), and the bounded complex of the c
Externí odkaz:
http://arxiv.org/abs/2404.03026
Which surfaces can be realized with two-dimensional faces of the five-dimensional cube (the penteract)? How can we visualize them? In recent work, Aveni, Govc, and Roldan, show that there exist 2690 connected closed cubical surfaces up to isomorphism
Externí odkaz:
http://arxiv.org/abs/2403.12825
We prove that, for each fixed genus, the portion of semigroups of that genus belonging to infinite chains in the semigroup tree approaches 0 as the genus grows to infinite. This means that most numerical semigroups have a finite number of descendants
Externí odkaz:
http://arxiv.org/abs/2401.18060
Autor:
Siegel, Aaron N.
The universe $\mathcal{E}$ of dead-ending partizan games has emerged as an important structure in the study of mis\`ere play. Here we attempt a systematic investigation of the structure of $\mathcal{E}$ and its subuniverses. We begin by showing that
Externí odkaz:
http://arxiv.org/abs/2312.16259
The notion of $S$-labeling of graphs, where $S$ is a subset of a symmetric group, was introduced in 2019 by Jin, Wong, and Zhu. This notion provides the framework for a common generalization of various well studied notions of graph coloring, includin
Externí odkaz:
http://arxiv.org/abs/2312.11744
How can we visualize all the surfaces that can be made from the faces of the tesseract? In recent work, Aveni, Govc, and Rold\'an showed that the torus and the sphere are the only closed surfaces that can be realized by a subset of two-dimensional fa
Externí odkaz:
http://arxiv.org/abs/2311.06596
Autor:
Godbole, Anant, Swickheimer, Hannah
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, vol. 26:1, Permutation Patterns 2023, Special issues (May 3, 2024) dmtcs:12458
Let $\pi_n$ be a uniformly chosen random permutation on $[n]$. Using an analysis of the probability that two overlapping consecutive $k$-permutations are order isomorphic, the authors of a recent paper showed that the expected number of distinct cons
Externí odkaz:
http://arxiv.org/abs/2310.14071