2006/12/28 by Thomas Lam, Lam, Thomas, Pavlo Pylyavskyy +1 · 1 citation
Mathematics · #05A15 #05E10 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.math/0612842
openalex publication_date 2006/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study pfaffian analogues of immanants, which we call pfaffinants. Our main object is the TL-pfaffinants which are analogues of Rhoades and Skandera's TL-immanants. We show that TL-pfaffinants are positive when applied to planar networks and explain how to decompose products of complementary pfaffians in terms of TL-pfaffinants. We conjecture in addition that TL-pfaffinants have positivity properties related to Schur Q-functions.