Current Search: Combinatorics Collection (x)


Title

Combinations and permutations (of various number of elements).

Abstract/Description

Listing of combinations of elements AF, with AF in terms of ad. 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 16 to permutations of four elements chosen from four (hard to read).

Identifier

FSUDirac_12_1e_0002

Format

Set of related objects


Title

Comparing coefficients of terms of expansions.

Abstract/Description

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?)

Identifier

FSUDirac_12_1d_0011

Format

Set of related objects


Title

Equations composed of terms of degree 4.

Abstract/Description

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).

Identifier

FSUDirac_12_1d_0010

Format

Set of related objects


Title

Investigating permutations.

Abstract/Description

Expansions of summations of cubic and quintic expressions; Counting permutations of three elements from possible five.

Identifier

FSUDirac_12_1a_0001

Format

Set of related objects


Title

Investigating permutations of five terms.

Abstract/Description

Listing of permutations of five elements chosen out of five; Sketches of graphs connecting five elements represented by nodes.

Identifier

FSUDirac_12_1a_0013

Format

Set of related objects


Title

List of permultations of five elements chosen from five: Multiple representations.

Abstract/Description

Listing of permutations of five elements chosen from five (similar to FSUDirac_12_1d_0014).

Identifier

FSUDirac_12_1e_0021

Format

Set of related objects


Title

Listing of permutations: Five elements chosen from five  I.

Abstract/Description

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 thirddegree expressions in five variables.

Identifier

FSUDirac_12_1a_0018

Format

Set of related objects


Title

Listing of permutations: Five elements chosen from five  II.

Abstract/Description

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)

Identifier

FSUDirac_12_1d_0014

Format

Set of related objects


Title

Permutations and coefficients of five elements.

Abstract/Description

Writing permutations of five elements 15 with repetition; listing oneterm expressions with coefficients summing to certain numbers; expanding different powers of an expression α.

Identifier

FSUDirac_12_1d_0028

Format

Set of related objects


Title

Permutations of four elements.

Abstract/Description

Writing permutations of four elements 14 with repetition.

Identifier

FSUDirac_12_1d_0026

Format

Set of related objects


Title

Permutations: four chosen from four; five chosen from five.

Abstract/Description

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 15 used as well).

Identifier

FSUDirac_12_1e_0020

Format

Set of related objects


Title

Permutations: three chosen from four, with powers of 2.

Abstract/Description

Listing permutations of three elements chosen from four, two of which are squared (elements ad); expansions of summations of quintic expressions in terms of ad.

Identifier

FSUDirac_12_1e_0012

Format

Set of related objects


Title

Possible identification of roots of a given quartic equation.

Abstract/Description

Possible evaluation of roots of certain quartic (?) polynomials (appears to be continued on FSUDirac_12_1d_0023); counting possible permutations of first four integers.

Identifier

FSUDirac_12_1d_0021

Format

Set of related objects


Title

Product of terms set equal to simple sums.

Abstract/Description

Finding products of terms eh, 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).

Identifier

FSUDirac_12_1e_0023

Format

Set of related objects


Title

Sums of fifthdegree terms.

Abstract/Description

Creating combinations of multiterm expressions made up of products and sum of six elements AF, which are made up of strict patterns and summation, multiplication and exponentiation (third degree) of five elements ae; Graph sketch connecting two sets of five elements each; Listing of permutations of five elements chosen out of five (like FSUDirac_12_1a_0013).

Identifier

FSUDirac_12_1a_0014

Format

Set of related objects


Title

Table of coefficients for terms of degree 5.

Abstract/Description

Analysis of coefficients (?) of given terms in different expressions; Summations of coefficients; Counting numbers of terms attached to each coefficient.

Identifier

FSUDirac_12_1a_0006

Format

Set of related objects