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User:Charles R Greathouse IV/Keywords/Table
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Current | Keyword v. 1 | Keyword v. 2 | Keyword v. 3 | Keyword v. 4 | Description | Examples |
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add | add | add | additive sequences (a(mn) = a(m) + a(n), GCD(m,n) = 1) | |||
cadd | cadd | add-comp | completely additive sequences (a(mn) = a(m) + a(n)) | |||
mult | mult | mult | mult | multiplicative sequences (a(mn) = a(m) * a(n), GCD(m,n) = 1) | ||
mult | cmult | cmult | mult-comp | completely multiplicative sequences (a(mn) = a(m) * a(n)) | ||
div | div | div | divisibility sequences (m divides n implies a(m) divides a(n)) | |||
udiv | udiv | div-unit | unitary divisibility sequences (m exactly divides n implies a(m) exactly divides a(n)) | |||
strdiv | strdiv | div-strong | strong divisibility set-like sequences (mn is in the the sequence if m and n are in the sequence and GCD(m,n) = 1) | |||
cstrdiv | cstrdiv | div-strong-comp | completely strong divisibility set-like sequences (mn is in the the sequence if m and n are in the sequence) | |||
copr | copr | copr | coprimality sequences (GCD(m,n) = 1 implies GCD(a(m), a(n)) = 1) | |||
ccopr | ccopr | copr-comp | complete coprimality sequences (GCD(a(m), a(n)) = 1, m ≠ n) | A000215 | ||
base | base:1-Rom | base-1-Rom | base-alt-Rom | Roman numerals dependent sequences | ||
base | base:2 | base-2 | base-2 | base 2 dependent sequences | ||
base | base:3 | base-3 | base-3 | base 3 dependent sequences | ||
base | base:bal-3 | base-bal-3 | base-bal-3 | base 3 (balanced) dependent sequences | ||
base | base:10 | base-10 | base-10 | base 10 dependent sequences | ||
base | base:16 | base-16 | base-16 | base 16 dependent sequences | ||
base | base:mix-fact | base-mix-fact | base-mix-fact | mixed base (factorial) dependent sequences | ||
base | base:mix-prim | base-mix-prim | base-mix-prim | mixed base (primorial) dependent sequences | ||
base | base:alt-phi | base-alt-phi | base-alt-phi | alternate bases (phinary) dependent sequences | ||
fini:no | fini-no | fini-no | infinite sequences | |||
fini:no? | fini-no? | fini-no? | conjectured infinite sequences | |||
fini:? | fini? | fini? | unknown whether finite or infinite sequences | |||
fini | fini:yes? | fini-yes? | fini-yes? | conjectured finite sequences | ||
fini | fini:yes | fini-yes | fini-yes | finite sequences | ||
fini | fini:yes-N | fini-yes-N | fini-yes-N | N terms finite sequences | ||
fini, full | fini:yes-full | fini-yes-full | fini-full | Finite sequences (all terms given) | ||
fini, full | fini:yes-N-full | fini-yes-N-full | fini-full, fini-yes-N | N terms finite sequences (all N terms given) | ||
frac | frac-num | frac-num | frac-num | fractions numerators | ||
frac | conv-num | conv-num | frac-num, conv | convergents (of continued fractions) numerators | ||
frac | frac-den | frac-den | frac-den | fractions denominators | ||
frac | conv-den | conv-den | frac-den, conv | convergents (of continued fractions) denominators | ||
cons | cmplx-re | cmplx-r | cmplx-0 | real part of complex numbers | ||
cons | cmplx-im | cmplx-i | cmplx-1 | imaginary part of complex numbers | ||
cons | quat-re | quat-r | quat-0 | real part of quaternions | ||
cons | quat-im-i | quat-i | quat-1 | imaginary i part of quaternions | ||
cons | quat-im-j | quat-j | quat-2 | imaginary j part of quaternions | ||
cons | quat-im-k | quat-k | quat-3 | imaginary k part of quaternions | ||
cons | oct-re, oct-im-1 to oct-im-7 | oct-r, oct-i-1 to oct-i-7 | oct-0, oct-1 to oct-7 | octonions | ||
cons | sed-re, sed-im-1 to sed-im-15 | sed-r, sed-i-1 to sed-i-15 | sed-0, sed-1 to sed-15 | sedenions | ||
1to1 | 1to1 | 1to1 | One-to-one with (one-to-one and onto, i.e. bijective, with a subset of ) | |||
prog | prog | fini-no, 1to1 | progressions: infinite one-to-one sequences (thus one-to-one and onto with ) | |||
mono:sincr | mono-sincr | mono-is | monotonic strictly increasing sequences (first differences > 0) | |||
mono:lincr | mono-lincr | mono-iw | monotonic weakly increasing sequences (first differences ≥ 0) | |||
mono:cons | mono-cons | mono-cons | constant sequences (first differences = 0) | |||
mono:ldecr | mono-ldecr | mono-dw | monotonic weakly decreasing sequences (first differences ≤ 0) | |||
mono:sdecr | mono-sdecr | mono-ds | monotonic strictly decreasing sequences (first differences < 0) | |||
conv | conv | conv | convex sequences (i.e. )
(second differences ≥ 0) (obeys Jensen’s inequality[2]) |
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conv:s | conv-s | conv-s | strictly convex sequences (i.e. )
(second differences > 0) (obeys Jensen’s strict inequality[2]) |
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arit | arit | arit | arithmetic sequences (i.e. )
(second differences = 0) |
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conc | conc | conc | concave sequences (i.e. )
(second differences < 0) |
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bounded:both | bounded-both | bounded-both | sequences with greatest lower bound and least upper bound | |||
bounded:above | bounded-above | bounded-above | sequences with least upper bound | |||
bounded:below | bounded-below | bounded-below | sequences with greatest lower bound | |||
bounded:none | bounded-none | bounded-none | unbounded sequences | |||
cons | cons:2 | cons-2 | real-2 | binary expansion of a constant | A104015 | |
cons | cons:3 | cons-3 | real-3 | ternary expansion of a constant | ||
cons | cons:bal-3 | cons-bal-3 | real-bal-3 | balanced ternary expansion of a constant | A129407 | |
cons | cons | cons | real-10 | decimal expansion of a constant | ||
cons | cons:16 | cons-16 | real-16 | hexadecimal expansion of a constant | ||
cofr | scofr | scofr | real, cofr | simple continued fraction expansion of a constant (partial quotients)
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gcofr-num or
gcofr-m |
gcofr-num or
gcofr-m |
real, gcofr-m | multiplicands in general continued fraction expansion of a constant (partial numerators)
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gcofr-den or
gcofr-a |
gcofr-den or
gcofr-a |
real, gcofr-a | addends in general continued fraction expansion of a constant (partial denominators)
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snrad:2 | snrad-2 | real, nrad | simple continued square root (nested square radicals) expansion of a constant
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snrad:3 | snrad-3 | real, nrad-3 | simple continued cubic root (nested cubic radicals) expansion of a constant
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gnrad:2-m | gnrad-2-m | real, gnrad-m | multiplicands in general continued square root (nested square radicals) expansion of a constant
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gnrad:2-a | gnrad-2-a | real, gnrad-a | addends in general continued square root (nested square radicals) expansion of a constant
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gnrad:3-m | gnrad-3-m | real, gnrad-3-m | multiplicands in general continued cubic root (nested cubic radicals) expansion of a constant
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gnrad:3-a | gnrad-3-a | real, gnrad-3-a | addends in general continued cubic root (nested cubic radicals) expansion of a constant
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ginrad:m | ginrad-m | real, ginrad-m | multiplicands in generalized indices continued root (nested radicals) expansion of a constant
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ginrad:a | ginrad-a | real, ginrad-a | addends in generalized indices continued root (nested radicals) expansion of a constant
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ginrad:i | ginrad-i | real, ginrad-i | indices in generalized indices continued root (nested radicals) expansion of a constant
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nonn | sign:pos | sign-pos | — | positive sequences | ||
nonn | sign:nneg | sign-nneg | — | nonnegative sequences | ||
nonn | sign:0 | sign-0 | — | the zero sequence | ||
sign | sign:npos | sign-npos | — | nonpositive sequences | ||
sign | sign:neg | sign-neg | — | negative sequences | ||
even | symm:even | symm-even | — | even sequences () | ||
odd | symm:odd | symm-odd | — | odd sequences () | ||
tabl | tabl:tri | tabl-tri | tabl-tri | table (triangular array) of numbers | ||
tabl | tabl:sq | tabl-sq | tabl-sq | table (square array) of numbers | ||
tabf | tabl:irr | tabl-irr | tabl | table (irregular array) of numbers | ||
hard | costly costly:time |
costly costly-time |
— | hard could be reserved for
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Notes
- ↑ The comma being used to separate distinct keywords.
- ↑ 2.0 2.1 Bjorn Poonen, Inequalities, © Berkeley Math Circle.