The Möbius function of factor order

AbstractIntervals in the factor ordering of a free monoid are investigated. It was shown by Farmer (1982) that such intervals (β, α) are contractible or homotopy spheres in case β is the empty word. We observe here that the same is true in general. This implies that the Möbius function of factor order takes values in {0, + 1, −1}. A recursive rule for this Möbius function is given, which allows efficient computation via the Knuth—Morris—Pratt algorithm.The Möbius function of subword order was studied in Björner (1990). We give here a simpler proof (a parity-changing involution) for its combinatorial interpretation

Axial U(1)U(1) symmetry at high temperature in 2-flavor lattice QCD

We investigate the axial $U(1)_A$ symmetry breaking above the critical temperature in two-flavor lattice QCD. The ensembles are generated with dynamical M\"obius domain-wall or reweighted overlap fermions. The $U(1)_A$ susceptibility is extracted from the low-modes spectrum of the overlap Dirac eigenvalues. We show the quark mass and temperature dependences of $U(1)_A$ susceptibility. Our results at $T=220 \, \mathrm{MeV}$ imply that the $U(1)_A$ symmetry is restored in the chiral limit. Its coincidence with vanishing topological susceptibility is observed.Comment: 8 pages, 4 figures, Proceedings of the 35th International Symposium on Lattice Field Theory, June 18-24, 2017, Granada, Spai