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math.CO2020
Signed Alternating-runs enumeration in Classical Weyl Groups
Hiranya Kishore Dey, Sivaramakrishnan Sivasubramanian
The alternating-runs polynomial enumerates alternating runs in the symmetric group. There are three formulae for the number of permutations, in with …
math.CO2020
On the Alternating runs polynomial in type B and D Coxeter Groups
Hiranya Kishore Dey, Sivaramakrishnan Sivasubramanian
Wilf showed that the the alternating runs polynomial counting the number of permutations in the Symmetric group is divisible by where $m = \lfloor (n-2)/2 \rfloo…
math.CO2020
Eulerian Central Limit Theorems and Carlitz identities in positive elements of Classical Weyl Groups
Hiranya Kishore Dey, Sivaramakrishnan Sivasubramanian
Central Limit Theorems are known for the Eulerian statistic "descent" (or "excedance") in the symmetric group $\SSS_n$. Recently, Fulman, Kim, Lee and Petersen gave a Central Limit…