# Combinatorics Collection

Combinations and permutations (of various number of elements)
Summary: Listing of combinations of elements A-F, with A-F in terms of a-d. Listing of permutations of five elements chosen from five (similar to FSUDirac_12_1d_0012). Summations of fractions of different denominators in terms of m,n that equal 1. Attempt to sketch graph with at least 6 nodes. Apparent assignment of values 1-6 to permutations of four elements chosen from four (hard to read).
Comparing coefficients of terms of expansions
Summary: Comparison of coefficients of terms in expansions of different summations/products of summations (like FSUDirac_12_1a_0011; FSUDirac_12_1d_0005); writing summations of products as quintic polynomials after substitution; comparison of coefficients of summated expressions up to degree 5 and assignment of values to each equation (e.g. 1, -5, 5. Possibly tied to Galois groups?)
Equations composed of terms of degree 4
Summary: Comparison of coefficients of summated expressions up to degree 4 and assignment of values to each equation (e.g. 1, -4, 2, 4. Like FSUDirac_12_1d_0029).
Investigating permutations
Summary: Expansions of summations of cubic and quintic expressions; Counting permutations of three elements from possible five.
Investigating permutations of five terms
Summary: Listing of permutations of five elements chosen out of five; Sketches of graphs connecting five elements represented by nodes.
List of permultations of five elements chosen from five: Multiple representations
Summary: Listing of permutations of five elements chosen from five (similar to FSUDirac_12_1d_0014).
Listing of permutations: Five elements chosen from five - I
Summary: Listing of permutations of five elements chosen from five (see FSUDirac_12_1a_0013 and FSUDirac_12_1a_0014); Crossing out certain permutations; Sketches of shapes with numbered vertices; Expressions with summation of third-degree expressions in five variables.
Listing of permutations: Five elements chosen from five - II
Summary: Listing permutations of five elements chosen from five (like FSUDirac_12_1a_0013, FSUDirac_12_1a_0014 and FSUDirac_12_1a_0018); listing permutations of six elements chosen from six with corresponding graphs with nodes matching elements (page hard to read)
Permutations and coefficients of five elements
Summary: Writing permutations of five elements 1-5 with repetition; listing one-term expressions with coefficients summing to certain numbers; expanding different powers of an expression α.
Permutations of four elements
Summary: Writing permutations of four elements 1-4 with repetition.
Permutations: four chosen from four; five chosen from five
Summary: Listing of permutations of four elements chosen from four (similar to FSUDirac_12_1d_0012). Listing of permutation of five elements chosen from five (a,b,c,d,e, but numbers 1-5 used as well).
Permutations: three chosen from four, with powers of 2
Summary: Listing permutations of three elements chosen from four, two of which are squared (elements a-d); expansions of summations of quintic expressions in terms of a-d.
Possible identification of roots of a given quartic equation
Summary: Possible evaluation of roots of certain quartic (?) polynomials (appears to be continued on FSUDirac_12_1d_0023); counting possible permutations of first four integers.
Product of terms set equal to simple sums
Summary: Finding products of terms e-h, which are equal to simple summations of k,l,m,n. Assignment of constants to represent quotients of form ab/c (same quotients as on FSUDirac_12_1e_0009).
Sums of fifth-degree terms
Summary: Creating combinations of multi-term expressions made up of products and sum of six elements A-F, which are made up of strict patterns and summation, multiplication and exponentiation (third degree) of five elements a-e; Graph sketch connecting two sets of five elements each; Listing of permutations of five elements chosen out of five (like FSUDirac_12_1a_0013).
Table of coefficients for terms of degree 5
Summary: Analysis of coefficients (?) of given terms in different expressions; Summations of coefficients; Counting numbers of terms attached to each coefficient.