Plethystic Exponential Calculus and Characteristic Polynomials of Permutations

Machine Learning for Hilbert Series

“…Mathematically, Hilbert series (HS) provide a means of counting regular functions on varieties. Physically, they are used in a range of scenarios, including to count BPS operators [1][2][3][4][5][6], determine moduli spaces [7][8][9][10], find standard model invariants [11][12][13], deal with string compactifications [14], construct effective Lagrangians [15][16][17][18][19][20], as well as for a range of other quiver-related computations [21][22][23][24][25][26][27][28][29][30][31].…”