A conjecture of Stanley states that if the generating function of a poset P is symmetric, then in fact P belongs to the family of posets induced by some skew shape lambda/mu. In this paper we show that if the set L(P) of the linear extensions of a poset P is plactic-closed, then P is a poset induced by a skew shape.
P-PARTITIONS AND THE PLACTIC CONGRUENCE / Malvenuto, Claudia. - In: GRAPHS AND COMBINATORICS. - ISSN 0911-0119. - STAMPA. - 9:1(1993), pp. 63-73. [10.1007/bf01195328]
P-PARTITIONS AND THE PLACTIC CONGRUENCE
MALVENUTO, Claudia
1993
Abstract
A conjecture of Stanley states that if the generating function of a poset P is symmetric, then in fact P belongs to the family of posets induced by some skew shape lambda/mu. In this paper we show that if the set L(P) of the linear extensions of a poset P is plactic-closed, then P is a poset induced by a skew shape.File allegati a questo prodotto
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