Congeneric Sequence

Congeneric sequence is an extreme case of Parial sequence where all non-empty elements are equals.

\(S_{c|T}\) is Congeneric sequence for T

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i1["1"] i2["2"] i3["3"] i4["4"] i5["5"] i6["6"] i7["7"] i8["8"] i9["9"] i10["10"] i11["11"] i12["12"]
i13["13"] i14["14"] i15["15"] i16["16"] i17["17"] i18["18"] i19["19"] i20["20"]
i21["21"] i22["22"] i23["23"] i24["24"] i25["25"] i26["26"] i27["27"]
i28["28"] i29["29"]

s1["-"] s2["-"] s3["T"] s4["-"] s5["-"] s6["-"] s7["-"] s8["-"] s9["-"] s10["-"]
s11["-"] s12["-"] s13["-"] s14["-"] s15["-"] s16["-"] s17["T"] s18["-"] s19["-"] s20["-"]
s21["-"] s22["-"] s23["-"] s24["-"] s25["-"] s26["T"] s27["-"] s28["-"] s29["T"]

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class i21,i22,i23,i24,i25,i26,i27,i28,i29 index

Mathematical Definition

Let \(X\) is Carrier Set

Let \(X_{-}\) is Partial Carrier Set

\[X \subset X_{-}\]

Let \(S_p\) is Partial sequence \(S_p : \{1, ..., l\} \longrightarrow X_{-},\)

\(S_p\) is called \(S_{c|e}\) - Congeneric sequence of \(e\) element - if \(\exists e \in X\Big|\forall i, S_{p}(i) \in \{-, e\}\)