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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…
math.CO2024
Unimodality and peak location of the characteristic polynomials of two distance matrices of trees
Rakesh Jana, Iswar Mahato, Sivaramakrishnan Sivasubramanian
Unimodality of the normalized coefficients of the characteristic polynomial of distance matrices of trees are known and bounds on the location of its peak (the largest coefficient)…
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 on permutations in . Two other studied statistics on are…