Umesh Shankar

collaborators

4 papers

math.CO2024

Two bijections in the spirit of the transformation fondamentale

Umesh Shankar

In this short paper, we give bijective proofs of two recent equidistribution results connecting cyclic and linear statistics in the spirit of the Foata's ``transformation fondament…

math.CO2024

Synchronicity of descent and excedance enumerators in the alternating subgroup

Umesh Shankar

Generalising the work of Dey, we define the notion of ultra-synchronicity of sequences of real numbers. Let $B_{n, k}, C_{n, k}, P_{n, k}, Q_{n, k}$ be the number of even permutations wit…

math.CO2024

Canonical reduced words and signed descent length enumeration in Coxeter groups

Umesh Shankar, Sivaramakrishnan Sivasubramanian

Reifegerste and independently, Petersen and Tenner studied a statistic $drops ()$ on permutations in $S_{n}$ . Two other studied statistics on $S_{n}$ are…

math.CO2023

Enumeration of flattened $k$ -Stirling permutations with respect to descents

Umesh Shankar

A $k$ -Stirling permutation of order $n$ is said to be "flattened" if the leading terms of its increasing runs are in ascending order. We show that flattened $k$ -Stirling permutatio…

Two bijections in the spirit of the transformation fondamentale

Synchronicity of descent and excedance enumerators in the alternating subgroup

Canonical reduced words and signed descent length enumeration in Coxeter groups

Enumeration of flattened k-Stirling permutations with respect to descents

Enumeration of flattened $k$ -Stirling permutations with respect to descents