19 citations · 93 across the 45 of their papers we have counts for
39 papers · 1 filter
A Lower Bound on the Expected Number of Distinct Patterns in a Random Permutation
Verónica Borrás-Serrano, Isabel Byrne, Anant Godbole +1
Let be a uniformly chosen random permutation on . The authors of [2] showed that the expected number of distinct consecutive patterns of all lengths $k\in\{1,2,\ldots,n\…
A Resolution of the McCarty Conjecture
Anant Godbole, Lybitina Koene, Grant Shirley
The McCarty Conjecture states that any McCarty Matrix (an matrix with positive integer entries and each of the row and column sums equal to ), can be additi…
No-Three-in-a- Variations on the No-Three-in-a-Line Problem
Natalie Dodson, Anant Godbole, Dashleen Gonzalez +2
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 grid such that no three of them form…
An Alternative Proof for the Expected Number of Distinct Consecutive Patterns in a Random Permutation
Anant Godbole, Hannah Swickheimer
Let be a uniformly chosen random permutation on . Using an analysis of the probability that two overlapping consecutive -permutations are order isomorphic, the author…
The Expected Number of Distinct Consecutive Patterns in a Random Permutation
Austin Allen, Dylan Cruz Fonseca, Veronica Dobbs +6
Let be a uniformly chosen random permutation on . Using an analysis of the probability that two overlapping consecutive -permutations are order isomorphic, we show th…
Graph Universal Cycles of Combinatorial Objects
Amelia Cantwell, Juliann Geraci, Anant Godbole +1
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…