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Combinatorics Collection

Permalink: https://diginole.lib.fsu.edu/islandora/object/fsu:diraccombinatorics
Combinations and permutations (of various number of elements)
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
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
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
Investigating permutations
Summary: Expansions of summations of cubic and quintic expressions; Counting permutations of three elements from possible five.
Investigating permutations of five terms
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
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
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
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
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
Permutations of four elements
Summary: Writing permutations of four elements 1-4 with repetition.
Permutations: four chosen from four; five chosen from five
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
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
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
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
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
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.