Andrew Beveridge

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20242026

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math.CO2026

Maximal Lehmer Codes for Permutations with Classical and Consecutive 321-Avoidance

Andrew Beveridge, Yufan Hu, Yucheng Liu

Let $S_{n} (321)$ and $S_{n} (321)$ denote the sets of $n$ -permutations avoiding the classical pattern $321$ and the consecutive pattern $321$ , respectively.…

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…