Signed differential posets and sign-imbalance

Authors:
Thomas Lam
Affiliations:
Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
Venue:
Journal of Combinatorial Theory Series A
Year:
2008

Citing 10
Cited 1

Enumerative combinatorics

Enumerative combinatorics
Further combinatorial properties of two Fibonacci lattices

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Generating linear extensions of posets by transpositions

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Duality of Graded Graphs

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Schensted Algorithms for Dual Graded Graphs

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Sign-balanced posets

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Growth diagrams, domino insertion and sign-imbalance

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On the sign-imbalance of partition shapes

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Rook numbers and the normal ordering problem

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On the sign-imbalance of skew partition shapes

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Skew domino Schensted correspondence and sign-imbalance

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Abstract

We study signed differential posets, a signed version of differential posets. These posets satisfy enumerative identities which are signed analogues of those satisfied by differential posets. Our main motivations are the sign-imbalance identities for partition shapes originally conjectured by Stanley, now proven in [T. Lam, Growth diagrams, domino insertion and sign-imbalance, J. Combin. Theory Ser. A 107 (2004) 87-115; A. Reifergerste, Permutation sign under the Robinson-Schensted-Knuth correspondence, Ann. Comb. 8 (2004) 103-112; J. Sjostrand, On the sign-imbalance of partition shapes, J. Combin. Theory Ser. A 111 (2005) 190-203]. We show that these identities result from a signed differential poset structure on Young's lattice, and explain similar identities for Fibonacci shapes.