TY - JOUR
T1 - Unimodality of Eulerian quasisymmetric functions
AU - Henderson, Anthony
AU - Wachs, Michelle L.
N1 - Funding Information:
E-mail addresses: anthony.henderson@sydney.edu.au (A. Henderson), wachs@math.miami.edu (M.L. Wachs). 1 Supported in part by Australian Research Council grant DP0985184. 2 Supported in part by National Science Foundation grant DMS 0902323.
PY - 2012/1
Y1 - 2012/1
N2 - We prove two conjectures of Shareshian and Wachs about Eulerian quasisymmetric functions and Eulerian polynomials. The first states that the cycle type Eulerian quasisymmetric function Qλ,j is Schur-positive, and moreover that the sequence Qλ,j as j varies is Schur-unimodal. The second conjecture, which we prove using the first, states that the cycle type (q, p)-Eulerian polynomial Aλmaj,des,exc(q,p,q-1t) is t-unimodal.
AB - We prove two conjectures of Shareshian and Wachs about Eulerian quasisymmetric functions and Eulerian polynomials. The first states that the cycle type Eulerian quasisymmetric function Qλ,j is Schur-positive, and moreover that the sequence Qλ,j as j varies is Schur-unimodal. The second conjecture, which we prove using the first, states that the cycle type (q, p)-Eulerian polynomial Aλmaj,des,exc(q,p,q-1t) is t-unimodal.
KW - Cycle type
KW - Eulerian polynomials
KW - Permutation statistics
KW - Symmetric functions
KW - Unimodality
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U2 - 10.1016/j.jcta.2011.07.004
DO - 10.1016/j.jcta.2011.07.004
M3 - Article
AN - SCOPUS:80052092606
VL - 119
SP - 135
EP - 145
JO - Journal of Combinatorial Theory - Series A
JF - Journal of Combinatorial Theory - Series A
SN - 0097-3165
IS - 1
ER -