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math.CO2025
Ordinal and disjoint sums of partially ordered patterns
Sucharita Biswas, Umesh Shankar, Sivaramakrishnan Sivasubramanian
Partially ordered patterns (POPs) generalize the classical notion of permutation patterns within the framework of pattern avoidance. Building on recent work by Burstein, Han, Kitae…
math.CO2025
Log-concavity of rows of triangular arrays satisfying a certain super-recurrence
Umesh Shankar
Recurrences of the form \begin{equation*} T(n,k) = (αn+βk +γ) \ T(n-1,k) + (α'n+β'k+γ')\ T(n-1,k-1)+δ_{n,0}δ_{k,0}. \end{equation*} show up as the recurrence for many well-studied…