Poincar� Polynomials of Odd Diagram Classes
N Fan, P Guo�- SIAM Journal on Discrete Mathematics, 2022 - SIAM
N Fan, P Guo
SIAM Journal on Discrete Mathematics, 2022•SIAMAn odd diagram class is a set of permutations with the same odd diagram. Brenti, Carnevale,
and Tenner Comb. Theory, 2 (2022), 13 showed that each odd diagram class is an interval
in the Bruhat order. They conjectured that such intervals are rank-symmetric. In this paper,
we present an algorithm to partition an odd diagram class in a uniform manner. As an
application, we obtain that the Poincaré polynomial of an odd diagram class factors into
polynomials of the form 1+t+⋯+t^m. This, in particular, resolves the conjecture of Brenti�…
and Tenner Comb. Theory, 2 (2022), 13 showed that each odd diagram class is an interval
in the Bruhat order. They conjectured that such intervals are rank-symmetric. In this paper,
we present an algorithm to partition an odd diagram class in a uniform manner. As an
application, we obtain that the Poincaré polynomial of an odd diagram class factors into
polynomials of the form 1+t+⋯+t^m. This, in particular, resolves the conjecture of Brenti�…
An odd diagram class is a set of permutations with the same odd diagram. Brenti, Carnevale, and Tenner [Comb. Theory, 2 (2022), 13] showed that each odd diagram class is an interval in the Bruhat order. They conjectured that such intervals are rank-symmetric. In this paper, we present an algorithm to partition an odd diagram class in a uniform manner. As an application, we obtain that the Poincaré polynomial of an odd diagram class factors into polynomials of the form . This, in particular, resolves the conjecture of Brenti, Carnevale, and Tenner [Comb. Theory, 2 (2022), 13].
Society for Industrial and Applied MathematicsShowing the best result for this search. See all results