Umesh Shankar

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20242026

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12 papers · 1 filter

math.CO2026

Multivariate stability of powered triangular recurrences and parametrised Eulerian polynomials

Umesh Shankar

We prove multivariate stability for a class of affine triangular recurrences whose two coefficients are raised to an arbitrary positive integer power. The variables keep track of c…

math.CO2026

Matchings and shape-Wilf-Equivalence of sets of patterns of length three I: Triples

Sucharita Biswas, Umesh Shankar, Sivaramakrishnan Sivasubramanian

Permutation pattern avoidance on Ferrers boards has become a central topic in enumerative combinatorics with important connections to matchings, set partitions, and other combinato…

math.CO2026

Avoiding patterns with three distinct letters in Canon permutations

Umesh Shankar

We study avoidance of patterns of length $3$ with three distinct letters in canon permutations. We reduce the problem to studying pattern avoidance in lattice words and show that t…

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…