Umesh Shankar

activity

20242026

collaborators

6 papers

math.CO2026

Caged subsequences in permutations

Niranjan Balachandran, Omkar Ramdas, Umesh Shankar

Given a sequence $a := (a_{1}, \dots, a_{n})$ of reals, a subsequence $b = (a_{i_{1}}, \dots, a_{i_{k}})$ is said to be "caged" if the largest and smallest among the member…

math.CO2026

Oddtown and eventown theorems for lattice paths

Umesh Shankar

For North-East lattice paths (which we simply call lattice paths), we define intersection in terms of common edges. We prove that a family of paths from $(0, 0)$ to $(n, n)$ in which…

math.CO2026

Homogenized Graphical Shi Arrangements and Deformed Dumont Permutations

Sauvik Poddar, Rutuja Sawant, Umesh Shankar

We introduce the homogenized graphical Shi arrangement associated with a simple undirected graph $G$ , which serves as a broad generalization of classical deformations of the braid…

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) = (Î±n+Î²k +Î³) \ T(n-1,k) + (Î±'n+Î²'k+Î³')\ T(n-1,k-1)+Î´_{n,0}Î´_{k,0}. \end{equation*} show up as the recurrence for many well-…

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…