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of 231
pro vyhledávání: '"Godbole, Anant"'
We pose a natural generalization to the well-studied and difficult no-three-in-a-line problem: How many points can be chosen on an $n \times n$ grid such that no three of them form an angle of $\theta$? In this paper, we classify which angles yield n
Externí odkaz:
http://arxiv.org/abs/2311.13183
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
Autor:
Allen, Austin, Fonseca, Dylan Cruz, Dobbs, Veronica, Downs, Egypt, Fokuoh, Evelyn, Godbole, Anant, Costa, Sebastián Papanikolaou, Soto, Christopher, Yoshikawa, Lino
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, we show that the expected number of distinct consecutive patterns in $\pi_n$ i
Externí odkaz:
http://arxiv.org/abs/2011.12179
A connected digraph in which the in-degree of any vertex equals its out-degree is Eulerian; this baseline result is used as the basis of existence proofs for universal cycles (also known as ucycles or generalized deBruijn cycles or U-cycles) of sever
Externí odkaz:
http://arxiv.org/abs/1911.07905
Mathematicians have traditionally been a select group of academics that produce high-impact ideas allowing substantial results in several fields of science. Throughout the past 35 years, undergraduates enrolling in mathematics or statistics have repr
Externí odkaz:
http://arxiv.org/abs/1907.12153
Using standard methods (due to Janson, Stein-Chen, and Talagrand) from probabilistic combinatorics, we explore the following general theme: As one progresses from each member of a family of objects ${\cal A}$ being "covered" by at most one object in
Externí odkaz:
http://arxiv.org/abs/1803.09601
Autor:
Cassels, Joshua, Godbole, Anant
Covering arrays for words of length $t$ over a $d$ letter alphabet are $k \times n$ arrays with entries from the alphabet so that for each choice of $t$ columns, each of the $d^t$ $t$-letter words appears at least once among the rows of the selected
Externí odkaz:
http://arxiv.org/abs/1803.06507
Autor:
Gardner, KB, Godbole, Anant
A connected digraph in which the in-degree of any vertex equals its out-degree is Eulerian, this baseline result is used as the basis of existence proofs for universal cycles (also known as generalized deBruijn cycles or U-cycles) of several combinat
Externí odkaz:
http://arxiv.org/abs/1711.07029
A set $\mathcal{A}$ is said to be an additive $h$-basis if each element in $\{0,1,\ldots,hn\}$ can be written as an $h$-sum of elements of $\mathcal{A}$ in {\it at least} one way. We seek multiple representations as $h$-sums, and, in this paper we ma
Externí odkaz:
http://arxiv.org/abs/1705.05198
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, Vol. 19 no. 2, Permutation Patterns 2016, Permutation Patterns (June 26, 2018) dmtcs:3287
When considering binary strings, it's natural to wonder how many distinct subsequences might exist in a given string. Given that there is an existing algorithm which provides a straightforward way to compute the number of distinct subsequences in a f
Externí odkaz:
http://arxiv.org/abs/1704.08661