History of Power sum symmetric polynomials $p_k$

 - combinatorics - algebra+- bases for symmetric polynomials Programs:   program-sage:

       \             # the next degree after this table" Numbers:-- params:-    n: '1'-    k: '1'-  number: x1-- params:-    n: '1'-    k: '2'-  number: x1^2-- params:-    n: '1'-    k: '3'-  number: x1^3-- params:-    n: '1'-    k: '4'-  number: x1^4-- params:-    n: '1'-    k: '5'-  number: x1^5-- params:-    n: '1'-    k: '6'-  number: x1^6-- params:-    n: '1'-    k: '7'-  number: x1^7-- params:-    n: '1'-    k: '8'-  number: x1^8-- params:-    n: '1'-    k: '9'-  number: x1^9-- params:-    n: '1'-    k: '10'-  number: x1^10-- params:-    n: '1'-    k: '11'-  number: x1^11-- params:-    n: '1'-    k: '12'-  number: x1^12-- params:-    n: '2'-    k: '1'-  number: x1 + x2-- params:-    n: '2'-    k: '2'-  number: x1^2 + x2^2-- params:-    n: '2'-    k: '3'-  number: x1^3 + x2^3-- params:-    n: '2'-    k: '4'-  number: x1^4 + x2^4-- params:-    n: '2'-    k: '5'-  number: x1^5 + x2^5-- params:-    n: '2'-    k: '6'-  number: x1^6 + x2^6-- params:-    n: '2'-    k: '7'-  number: x1^7 + x2^7-- params:-    n: '2'-    k: '8'-  number: x1^8 + x2^8-- params:-    n: '2'-    k: '9'-  number: x1^9 + x2^9-- params:-    n: '2'-    k: '10'-  number: x1^10 + x2^10-- params:-    n: '2'-    k: '11'-  number: x1^11 + x2^11-- params:-    n: '2'-    k: '12'-  number: x1^12 + x2^12-- params:-    n: '3'-    k: '1'-  number: x1 + x2 + x3-- params:-    n: '3'-    k: '2'-  number: x1^2 + x2^2 + x3^2-- params:-    n: '3'-    k: '3'-  number: x1^3 + x2^3 + x3^3-- params:-    n: '3'-    k: '4'-  number: x1^4 + x2^4 + x3^4-- params:-    n: '3'-    k: '5'-  number: x1^5 + x2^5 + x3^5-- params:-    n: '3'-    k: '6'-  number: x1^6 + x2^6 + x3^6-- params:-    n: '3'-    k: '7'-  number: x1^7 + x2^7 + x3^7-- params:-    n: '3'-    k: '8'-  number: x1^8 + x2^8 + x3^8-- params:-    n: '3'-    k: '9'-  number: x1^9 + x2^9 + x3^9-- params:-    n: '3'-    k: '10'-  number: x1^10 + x2^10 + x3^10-- params:-    n: '3'-    k: '11'-  number: x1^11 + x2^11 + x3^11-- params:-    n: '3'-    k: '12'-  number: x1^12 + x2^12 + x3^12-- params:-    n: '4'-    k: '1'-  number: x1 + x2 + x3 + x4-- params:-    n: '4'-    k: '2'-  number: x1^2 + x2^2 + x3^2 + x4^2-- params:-    n: '4'-    k: '3'-  number: x1^3 + x2^3 + x3^3 + x4^3-- params:-    n: '4'-    k: '4'-  number: x1^4 + x2^4 + x3^4 + x4^4-- params:-    n: '4'-    k: '5'-  number: x1^5 + x2^5 + x3^5 + x4^5-- params:-    n: '4'-    k: '6'-  number: x1^6 + x2^6 + x3^6 + x4^6-- params:-    n: '4'-    k: '7'-  number: x1^7 + x2^7 + x3^7 + x4^7-- params:-    n: '4'-    k: '8'-  number: x1^8 + x2^8 + x3^8 + x4^8-- params:-    n: '4'-    k: '9'-  number: x1^9 + x2^9 + x3^9 + x4^9-- params:-    n: '4'-    k: '10'-  number: x1^10 + x2^10 + x3^10 + x4^10-- params:-    n: '4'-    k: '11'-  number: x1^11 + x2^11 + x3^11 + x4^11-- params:-    n: '4'-    k: '12'-  number: x1^12 + x2^12 + x3^12 + x4^12-- params:-    n: '5'-    k: '1'-  number: x1 + x2 + x3 + x4 + x5-- params:-    n: '5'-    k: '2'-  number: x1^2 + x2^2 + x3^2 + x4^2 + x5^2-- params:-    n: '5'-    k: '3'-  number: x1^3 + x2^3 + x3^3 + x4^3 + x5^3-- params:-    n: '5'-    k: '4'-  number: x1^4 + x2^4 + x3^4 + x4^4 + x5^4-- params:-    n: '5'-    k: '5'-  number: x1^5 + x2^5 + x3^5 + x4^5 + x5^5-- params:-    n: '5'-    k: '6'-  number: x1^6 + x2^6 + x3^6 + x4^6 + x5^6-- params:-    n: '5'-    k: '7'-  number: x1^7 + x2^7 + x3^7 + x4^7 + x5^7-- params:-    n: '5'-    k: '8'-  number: x1^8 + x2^8 + x3^8 + x4^8 + x5^8-- params:-    n: '5'-    k: '9'-  number: x1^9 + x2^9 + x3^9 + x4^9 + x5^9-- params:-    n: '5'-    k: '10'-  number: x1^10 + x2^10 + x3^10 + x4^10 + x5^10-- params:-    n: '5'-    k: '11'-  number: x1^11 + x2^11 + x3^11 + x4^11 + x5^11-- params:-    n: '5'-    k: '12'-  number: x1^12 + x2^12 + x3^12 + x4^12 + x5^12-- params:-    n: '6'-    k: '1'-  number: x1 + x2 + x3 + x4 + x5 + x6-- params:-    n: '6'-    k: '2'-  number: x1^2 + x2^2 + x3^2 + x4^2 + x5^2 + x6^2-- params:-    n: '6'-    k: '3'-  number: x1^3 + x2^3 + x3^3 + x4^3 + x5^3 + x6^3-- params:-    n: '6'-    k: '4'-  number: x1^4 + x2^4 + x3^4 + x4^4 + x5^4 + x6^4-- params:-    n: '6'-    k: '5'-  number: x1^5 + x2^5 + x3^5 + x4^5 + x5^5 + x6^5-- params:-    n: '6'-    k: '6'-  number: x1^6 + x2^6 + x3^6 + x4^6 + x5^6 + x6^6-- params:-    n: '6'-    k: '7'-  number: x1^7 + x2^7 + x3^7 + x4^7 + x5^7 + x6^7-- params:-    n: '6'-    k: '8'-  number: x1^8 + x2^8 + x3^8 + x4^8 + x5^8 + x6^8-- params:-    n: '6'-    k: '9'-  number: x1^9 + x2^9 + x3^9 + x4^9 + x5^9 + x6^9-- params:-    n: '6'-    k: '10'-  number: x1^10 + x2^10 + x3^10 + x4^10 + x5^10 + x6^10-- params:-    n: '6'-    k: '11'-  number: x1^11 + x2^11 + x3^11 + x4^11 + x5^11 + x6^11-- params:-    n: '6'-    k: '12'-  number: x1^12 + x2^12 + x3^12 + x4^12 + x5^12 + x6^12+  '1':+    '1': x1+    '2': x1^2+    '3': x1^3+    '4': x1^4+    '5': x1^5+    '6': x1^6+    '7': x1^7+    '8': x1^8+    '9': x1^9+    '10': x1^10+    '11': x1^11+    '12': x1^12+  '2':+    '1': x1 + x2+    '2': x1^2 + x2^2+    '3': x1^3 + x2^3+    '4': x1^4 + x2^4+    '5': x1^5 + x2^5+    '6': x1^6 + x2^6+    '7': x1^7 + x2^7+    '8': x1^8 + x2^8+    '9': x1^9 + x2^9+    '10': x1^10 + x2^10+    '11': x1^11 + x2^11+    '12': x1^12 + x2^12+  '3':+    '1': x1 + x2 + x3+    '2': x1^2 + x2^2 + x3^2+    '3': x1^3 + x2^3 + x3^3+    '4': x1^4 + x2^4 + x3^4+    '5': x1^5 + x2^5 + x3^5+    '6': x1^6 + x2^6 + x3^6+    '7': x1^7 + x2^7 + x3^7+    '8': x1^8 + x2^8 + x3^8+    '9': x1^9 + x2^9 + x3^9+    '10': x1^10 + x2^10 + x3^10+    '11': x1^11 + x2^11 + x3^11+    '12': x1^12 + x2^12 + x3^12+  '4':+    '1': x1 + x2 + x3 + x4+    '2': x1^2 + x2^2 + x3^2 + x4^2+    '3': x1^3 + x2^3 + x3^3 + x4^3+    '4': x1^4 + x2^4 + x3^4 + x4^4+    '5': x1^5 + x2^5 + x3^5 + x4^5+    '6': x1^6 + x2^6 + x3^6 + x4^6+    '7': x1^7 + x2^7 + x3^7 + x4^7+    '8': x1^8 + x2^8 + x3^8 + x4^8+    '9': x1^9 + x2^9 + x3^9 + x4^9+    '10': x1^10 + x2^10 + x3^10 + x4^10+    '11': x1^11 + x2^11 + x3^11 + x4^11+    '12': x1^12 + x2^12 + x3^12 + x4^12+  '5':+    '1': x1 + x2 + x3 + x4 + x5+    '2': x1^2 + x2^2 + x3^2 + x4^2 + x5^2+    '3': x1^3 + x2^3 + x3^3 + x4^3 + x5^3+    '4': x1^4 + x2^4 + x3^4 + x4^4 + x5^4+    '5': x1^5 + x2^5 + x3^5 + x4^5 + x5^5+    '6': x1^6 + x2^6 + x3^6 + x4^6 + x5^6+    '7': x1^7 + x2^7 + x3^7 + x4^7 + x5^7+    '8': x1^8 + x2^8 + x3^8 + x4^8 + x5^8+    '9': x1^9 + x2^9 + x3^9 + x4^9 + x5^9+    '10': x1^10 + x2^10 + x3^10 + x4^10 + x5^10+    '11': x1^11 + x2^11 + x3^11 + x4^11 + x5^11+    '12': x1^12 + x2^12 + x3^12 + x4^12 + x5^12+  '6':+    '1': x1 + x2 + x3 + x4 + x5 + x6+    '2': x1^2 + x2^2 + x3^2 + x4^2 + x5^2 + x6^2+    '3': x1^3 + x2^3 + x3^3 + x4^3 + x5^3 + x6^3+    '4': x1^4 + x2^4 + x3^4 + x4^4 + x5^4 + x6^4+    '5': x1^5 + x2^5 + x3^5 + x4^5 + x5^5 + x6^5+    '6': x1^6 + x2^6 + x3^6 + x4^6 + x5^6 + x6^6+    '7': x1^7 + x2^7 + x3^7 + x4^7 + x5^7 + x6^7+    '8': x1^8 + x2^8 + x3^8 + x4^8 + x5^8 + x6^8+    '9': x1^9 + x2^9 + x3^9 + x4^9 + x5^9 + x6^9+    '10': x1^10 + x2^10 + x3^10 + x4^10 + x5^10 + x6^10+    '11': x1^11 + x2^11 + x3^11 + x4^11 + x5^11 + x6^11+    '12': x1^12 + x2^12 + x3^12 + x4^12 + x5^12 + x6^12