6 papers
Reciprocity of Skew Hall-Littlewood-Schubert Series
Ron M. Adin, Tomer Bauer
Carnevale, Schein and Voll proved self-reciprocity of the generalized Igusa functions, and Maglione and Voll did the same for the Hall-Littlewood-Schubert series. We introduce a si…
Conjugating full cycles by adjacent transpositions: diameter and sorting time
Ron M. Adin, Eli Bagno, Yuval Roichman
We establish upper and lower bounds on the maximal number of steps needed to transform a cyclic permutation to the canonical cyclic permutation using conjugation by adjacent transp…
Asymptotics of higher Lie characters
Ron M. Adin, Yuval Roichman, Natalia Tsilevich
Higher Lie characters form a distinguished family of symmetric group characters, which appear in many areas of algebra and combinatorics. An old open problem of Thrall is to decomp…
Circular sorting
Ron M. Adin, Noga Alon, Yuval Roichman
We determine the maximal number of steps required to sort labeled points on a circle by adjacent swaps. Lower bounds for sorting by all swaps, not necessarily adjacent, are giv…
Descent set distribution for permutations with cycles of only odd or only even lengths
Ron M. Adin, Pál Hegedűs, Yuval Roichman
It is known that the number of permutations in the symmetric group with cycles of odd lengths only is equal to the number of permutations with cycles of even lengths only.…
Higher Lie characters and root enumeration in classical Weyl groups
Ron M. Adin, Pál Hegedüs, Yuval Roichman
We prove that, for any integer , the -th root enumerator in the classical Weyl group of type is a proper character. The proof uses higher Lie characters of type .