Andrew Beveridge

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20242026

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6 papers · 1 filter

math.CO2026

Lehmer Codes and the Reverse-Complement Mapping from (32-1)-Avoiding Permutations to (3-21)-Avoiding Permutations

Andrew Beveridge, Yufan Hu, Yucheng Liu

Let $S_{n} (32 - 1)$ and $S_{n} (3 - 21)$ denote the sets of $n$ -permutations avoiding the vincular patterns $32 - 1$ and $3 - 21$ , respectively. Using Lehmer codes,…

math.CO2026

(32-1)-Avoiding Permutations with Maximum Inversion Number

Andrew Beveridge, Kristin Heysse, Paige Robertson

A permutation $π \in S_{n}$ is (32-1)-avoiding when there do not exist $1 \leq i < i + 1 < j \leq n$ such that $π_{i} > π_{i + 1} > π_{j}$ . We determine the maximum inversion number for (32-1…

math.CO2026

Approval Ballot Triangles and Strict-Sense Ballots

Andrew Beveridge, Ian Calaway

We consider a family of binary triangular arrays, called approval ballot triangles (ABTs), that are in bijection with totally symmetric self-complementary plane partitions (TSSCPPs…

math.CO2025

Random Walks and the Best Meeting Time for Trees

Andrew Beveridge, Ari Holcombe Pomerance

We consider random walks on a tree $G = (V, E)$ with stationary distribution $π_{v} = deg (v) /2∣ E ∣$ for $v \in V$ . Let the hitting time $H (v, w)$ denote the expected number of st…

math.CO2025

Random Walks and the Meeting Time for Trees

Andrew Beveridge, Ben Bridenbaugh, Ari Holcombe Pomerance

Consider a random walk on a tree $G = (V, E)$ . For $v, w \in V$ , let the hitting time $H (v, w)$ denote the expected number of steps required for the random walk started at $v$ to reach…

math.CO2024

The Exact Mixing Time for Trees with Fixed Diameter

Andrew Beveridge, Kristin Heysse, Rhys O'Higgins +1

We characterize the extremal structure for the exact mixing time for random walks on trees $T_{n, d}$ of order $n$ with diameter $d$ . Given a graph $G = (V, E)$ , let $H (v, π)$ denote th…