Slick & Yo
In trying to determine the possible color results of a breeding it can be important to know not only the sire and dam's colors, but also the colors of their parents and the colors of any puppies they may have already produced

Slick - Bar'O's Ogeechee of O'run - gold brindle and white parti - sire = pale fawn and white parti & dam = brindle and white parti - we can expect from this that Slick carries non-brindle and probably c^ch - since his sire is a pale fawn

Yo - Owrun Youghiougheny- blue brindle, Irish Marked, mask - sire = red fawn & dam = red brindle with white - we can expect from this that Yo carries non-brindle. Yo is a rather "blurred" brindle, which is probably an expression of "sabling" that is also seen in her one sabled fawn son.

1

Note: yellow, red and fawn are "lumped" together genetically

A locus

Slick = A^yA^y(pure for fawn)
Yo = A^yA^y (pure for fawn)

C locus

Slick is a rich, golden brindle - but his sire is a pale fawn, and Yo is not a pale, silver blue - so we will assume the following:

Slick = Cc^ch (pure for complete expression of red/yellow and blue pigments - carrying Chinchilla)
Yo = CC (pure for complete expression of red/yellow and blue pigments)

D locus

We already know the Yo is blue and Slick is not. 9 puppies is a statistically large enough sample to assume that Slick does not carry the gene, since there were no blue brindle or blue fawn puppies:

Slick = DD (pure for non-blue)
Yo = dd (pure for blue)

E locus

Slick does not have a mask and Yo does, so we know she has that gene to contribute.

Slick = EE (not masked)
Yo = E^mE (masked, carrying not masked)

K locus

Since Slick and Yo are both brindles the neither can have the dominant K gene that produces blacks. Neither parent is either dominant black or its blue dilution, both are brindle but since they produced non-brindle we know both are not pure for brindle.

Slick = k^brk (brindle, carrying non-brindle)
Yo = k^brk (brindle, carrying non-brindle)

R locus

Since neither the parents nor any of the puppies are Roan we know the following:

Slick = rr (displays normal color and does not carry Roan)
Yo = rr (ditto)

S locus

We know from their appearance that Slick displays more white than does Yo, but the presence of the parti puppies shows that Yo carries that gene:

Slick = s^ps^p(pure for parti)
Yo = sⁱs^p (Irish Marked, carries parti)

T locus

Not enough data to tell.

All of this gives us the following analysis of the color genetics involved with these parents and their offspring:

Slick - Bar'O's Ogeechee of O'Run - gold brindle & white parti =A^yA^y Cc^ch DD EE k^brk rr s^ps^p
Yo-Owrun Youghiougheny-blue brindle,Irish Marked,mask = A^yA^y CC dd E^mE k^brk rr sⁱs^p

Genetic notation is simply a "short-hand" method of conveying information about the genes carried and/or displayed.  Dominant genes are noted as UPPERCASE and are listed first at each locus, when they are present. Recessive genes are noted as lower case and are listed second at each locus, when a dominant is present.  In the case of 2 dominants or 2 recessives at the same locus the one that is dominant over it's locus partner is listed first. Superscript letters provide father description of the particular gene's actions.  The above examples convey quick information about what colors these parents can be expected to produce:

Slick = A^yA^y Cc^ch DD EE k^brk rr s^ps^p

A^yA^y - pure for red/fawn
C = full expression of pigment, not "washed out" in shade
c^ch - carrying the Chinchilla gene for pale colors
DD = pure for non-blue
EE = allows expression of the black provided by DD & E^br genes
rr = not Roaned
k^br = allows the expression of black in the brindle/striped pattern
k = carrying non-brindle
s^ps^p = probably pure for parti

Yo = AyAy CC dd E^mE k^brk rr sⁱs^p

A^yA^y = pure for red/fawn
CC = full expression of pigment, not "washed out" in shade
dd = pure for the blue dilution
E^m = allows the expression of blue in the mask patterning
E^br = allows the expression of black in the brindle/striped pattern
k^br = allows the expression of black in the brindle/striped pattern
k = carrying non-brindle
rr = not Roaned
sⁱ = Irish Marked in her own color
sⁱ = carries the parti gene

red and white, Irish Marked - A^yA^y CC or c^ch Dd EE kk rr sⁱs^p
red and white, Irish Marked, black mask - A^yA^y CC or c^ch Dd EE^m kk rr sⁱs^p
fawn and white, parti = A^yA^y CCor c^ch Dd EE kk rr s^ps^p
fawn and white, parti, black mask = A^yA^y CCor c^ch Dd EE^m kk rr s^ps^p
brindle, Irish Marked - A^yA^y CCor c^ch Dd EE k^brk rr sⁱs^p
brindle, Irish Marked, black mask - A^yA^y CCor c^ch Dd EE^m k^brk rr sⁱs^p
brindle, parti, masked = A^yA^y CCor c^ch Dd EE^m k^brk rr s^ps^p
brindle, parti = A^yA^y CCor c^ch Dd EE k^brk rr s^ps^p

All of Slick and Yo's puppies will carry blue, since Yo has no other gene to contribute at that locus. Also the Irish Marked puppies will carry parti - as Slick has no other gene to contribute at that locus. Any of the puppies could be carrying the Chinchilla (c^ch) but they do not express it as Yo does not have a matching recessive that would allow it expression.