3/1/2007 · An enriched P -partition (respectively left enriched P -partition) is an order- preserving map f 😛 → X prime (respectively X (lscript) ) such that for all i jin Z. T.K. Petersen / Advances in Mathematics 209 (2007) 561–610 581 It is helpful to remember that enriched P -partitions .
It is helpful to remember that Stembridge’s enriched P-partitions are the nonzero left enriched P-partitions, i.e.
those for which f(i) 6=s0 for any i. We let E(PS) denote the set of all enriched P-partitions f : P ?S0 E(`)(PS) denotes the set of left enriched P-partitions .
In this paper, we introduce and develop a theory of enriched P-partitions like ordinary P-partitions, these are order-preserving maps from posets to chains, but with different rules governing the occurrence of equal values. The principal examples of enriched P-partitions given here are the tableaux associated with Schur’s Q-functions.
ring of quasisymmetric functions. Just as Stembridge’s enriched P-partitions connect with qua-sisymmetric functions (the dual coalgebra to Sol(An?1)), the new types of enriched P-partitions we present here connect to type B quasisymmetric functions (the dual coalgebra to Sol(Bn)),as studied by Chak-On Chow [15] using ordinary type B P-partitions. In Section 6, we will lay the, In this paper, we introduce and develop a theory of enriched P-partitions like ordinary P-partitions, these are order-preserving maps from posets to chains, but with different rules governing the occurrence of equal values. The principal examples of enriched P-partitions given here are the tableaux associated with Schur’s Q-functions.
9/1/2005 · Whereas Stembridge’s enriched P-partitions are related to quasisymmetric functions (the coalgebra dual to Solomon’s type A descent alge- bra), our generalized enriched P-partitions are related to…
our generalized enriched P-partitions are related to type B quasisymmetric functions (the coalgebra dual to Solomon’s t ype B descent algebra)..
8/1/2005 · Abstract: We develop a more general view of Stembridge’s enriched $P$-partitions and use this theory to outline the structure of peak algebras for the symmetric group …
Stembridge’s enriched P-partitions and gives results for the type A peak algebras. Chapter 4 introduces type B enriched P-partitions and the type B peak algebra. The results of chapters 3 and 4 can also be found in [Pet]. The remaining pages of this preface give a summary of the main results of this paper.
