3 papers
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…
math.CO2024
A descent-excedance correspondence in colored permutation groups
Hiranya Kishore Dey, Umesh Shankar, Sivaramakrishnan Sivasubramanian
It is well known that descents and excedances are equidistributed in the symmetric group. We show that the descent and excedance enumerators, summed over permutations with a fixed…