or Xglqt G qcq ipcq.es qq.TO ve E 2 Vz Case I X Cuz XCuz 0 g - PDF document

Colorings Chromatic Polynomial Formula DeletionContraction SymmetricChromaticFunction Stanley specialization Symmetry Deletion Contraction Coloring of a graph G X VG 1,2 17 9222 01 0 0 Ppezr coloring Hedges Lynde EGS 022 1 22 XLV tXCqj Howto count proper colorings ChromaticPolynomiat g I g I or Xglqt G qcq ipcq.es qq.TO ve E 2 Vz Case I X Cuz XCuz 0 g 10 g I qlq DLq.cl XH g H case xcua xcv 0 1 1 v 0 9cg174 234 2 3 q qCq1 Cq 1 qCq 1 g 2 Cq 2 Ed Special cases Recursive Method Deletion Contraction qtr 000 02 in Any proper coloring of G is also f e a proper coloring G However proper colorings of G e i true include cases where xcv xw

include cases here Xcv Xwa These are colorings when y Vz Ce contracted Xd g XG e.GL Xue q 11 ft 66 du du fo 9 o O O k b dy or ga O O O O G O O of q2 9 q2 If q3 q2 q2 q q2 q q3 3q2t2q g q q 1 Cq 2 Stanley Symmetric Chromatic Function Infinite colors gets 1 variable each color Xl Xz etc Xdr xz I xfzpert.IE x xz D xtxxj x.xxy ix.MX I Xo A t XXzXzt Xz Xy t XLI 0 A 1 2 3 X t XzXzXyt X ZX Xg 2 Xix Xk i j k i k canswitch aroundvariables and nothing Symmetric changes a sX

f EET let Xu for some n Specialization n 1 I Xun f I 0,0 I l l n Symmetric basis Power function basis Pk P _4 1 21 ok X Pk 1 24 Ps Xp X I X Xc xixjxki j tk.it k P n3 3h42m 3p Pz 2ps XiXjXk 3 XiXjXj 3 XiXjXj 1 Xi Xi 13 Xi Xi Xi Xi E 1 for Ken is Nole precisely preen specialization Pk xYtxEtxYt 147kt1kt 140kt i n n