Alphabet of Congeneric sequences

Alphabet of Congeneric sequences is an Alphabet.

Congeneric sequencesAlphabet and Congeneric sequencesAlphabet

block-beta
columns 31

space:2 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"]

space j1["1"] s1["I"] s2["-"] s3["-"] s4["-"] s5["-"] s6["-"] s7["I"] s8["-"] s9["-"] s10["-"]
s11["-"] s12["-"] s13["-"] s14["-"] s15["-"] s16["-"] s17["-"] s18["-"] s19["-"] s20["-"]
s21["-"] s22["-"] s23["-"] s24["-"] s25["-"] s26["-"] s27["-"] s28["-"] s29["-"]

space j2["2"] n1["-"] n2["N"] n3["-"] n4["-"] n5["-"] n6["-"] n7["-"] n8["-"] n9["-"] n10["N"]
n11["-"] n12["-"] n13["-"] n14["-"] n15["-"] n16["-"] n17["-"] n18["-"] n19["-"] n20["-"]
n21["-"] n22["-"] n23["-"] n24["-"] n25["-"] n26["-"] n27["-"] n28["-"] n29["-"]

space j3["3"] t1["-"] t2["-"] t3["T"] t4["-"] t5["-"] t6["-"] t7["-"] t8["-"] t9["-"] t10["-"]
t11["-"] t12["-"] t13["-"] t14["-"] t15["-"] t16["-"] t17["T"] t18["-"] t19["-"] t20["-"]
t21["-"] t22["-"] t23["-"] t24["-"] t25["-"] t26["T"] t27["-"] t28["-"] t29["T"]

space j4["4"] e1["-"] e2["-"] e3["-"] e4["E"] e5["-"] e6["-"] e7["-"] e8["-"] e9["E"] e10["-"]
e11["-"] e12["E"] e13["-"] e14["-"] e15["-"] e16["-"] e17["-"] e18["-"] e19["-"] e20["-"]
e21["-"] e22["-"] e23["-"] e24["-"] e25["-"] e26["-"] e27["-"] e28["-"] e29["-"]

space j5["5"] l1["-"] l2["-"] l3["-"] l4["-"] l5["L"] l6["L"] l7["-"] l8["-"] l9["-"] l10["-"]
l11["-"] l12["-"] l13["-"] l14["-"] l15["-"] l16["-"] l17["-"] l18["-"] l19["-"] l20["-"]
l21["-"] l22["-"] l23["-"] l24["L"] l25["-"] l26["-"] l27["-"] l28["-"] l29["-"]

space j6["6"] g1["-"] g2["-"] g3["-"] g4["-"] g5["-"] g6["-"] g7["-"] g8["G"] g9["-"] g10["-"]
g11["-"] g12["-"] g13["-"] g14["-"] g15["-"] g16["-"] g17["-"] g18["-"] g19["-"] g20["-"]
g21["-"] g22["-"] g23["-"] g24["-"] g25["-"] g26["-"] g27["-"] g28["-"] g29["-"]

space j7["7"] c1["-"] c2["-"] c3["-"] c4["-"] c5["-"] c6["-"] c7["-"] c8["-"] c9["-"] c10["-"]
c11["C"] c12["-"] c13["-"] c14["-"] c15["-"] c16["-"] c17["-"] c18["-"] c19["-"] c20["-"]
c21["-"] c22["-"] c23["-"] c24["-"] c25["-"] c26["-"] c27["-"] c28["-"] c29["-"]

space j8["8"] sp1["-"] sp2["-"] sp3["-"] sp4["-"] sp5["-"] sp6["-"] sp7["-"] sp8["-"] sp9["-"] sp10["-"]
sp11["-"] sp12["-"] sp13[" "] sp14["-"] sp15["-"] sp16[" "] sp17["-"] sp18["-"] sp19["-"] sp20[" "]
sp21["-"] sp22["-"] sp23["-"] sp24["-"] sp25["-"] sp26["-"] sp27["-"] sp28["-"] sp29["-"]

space j9["9"] b1["-"] b2["-"] b3["-"] b4["-"] b5["-"] b6["-"] b7["-"] b8["-"] b9["-"] b10["-"]
b11["-"] b12["-"] b13["-"] b14["-"] b15["-"] b16["-"] b17["-"] b18["-"] b19["-"] b20["-"]
b21["-"] b22["B"] b23["-"] b24["-"] b25["-"] b26["-"] b27["-"] b28["-"] b29["-"]

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class g1,g2,g3,g4,g5,g6,g7,g9,g10 index
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class c1,c2,c3,c4,c5,c6,c7,c8,c9,c10 index
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block-beta
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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"]

a1["I"] j1["1"] s1["I"] s2["-"] s3["-"] s4["-"] s5["-"] s6["-"] s7["I"] s8["-"] s9["-"] s10["-"]
s11["-"] s12["-"] s13["-"] s14["-"] s15["-"] s16["-"] s17["-"] s18["-"] s19["-"] s20["-"]
s21["-"] s22["-"] s23["-"] s24["-"] s25["-"] s26["-"] s27["-"] s28["-"] s29["-"]

a2["N"] j2["2"] n1["-"] n2["N"] n3["-"] n4["-"] n5["-"] n6["-"] n7["-"] n8["-"] n9["-"] n10["N"]
n11["-"] n12["-"] n13["-"] n14["-"] n15["-"] n16["-"] n17["-"] n18["-"] n19["-"] n20["-"]
n21["-"] n22["-"] n23["-"] n24["-"] n25["-"] n26["-"] n27["-"] n28["-"] n29["-"]

a3["T"] j3["3"] t1["-"] t2["-"] t3["T"] t4["-"] t5["-"] t6["-"] t7["-"] t8["-"] t9["-"] t10["-"]
t11["-"] t12["-"] t13["-"] t14["-"] t15["-"] t16["-"] t17["T"] t18["-"] t19["-"] t20["-"]
t21["-"] t22["-"] t23["-"] t24["-"] t25["-"] t26["T"] t27["-"] t28["-"] t29["T"]

a4["E"] j4["4"] e1["-"] e2["-"] e3["-"] e4["E"] e5["-"] e6["-"] e7["-"] e8["-"] e9["E"] e10["-"]
e11["-"] e12["E"] e13["-"] e14["-"] e15["-"] e16["-"] e17["-"] e18["-"] e19["-"] e20["-"]
e21["-"] e22["-"] e23["-"] e24["-"] e25["-"] e26["-"] e27["-"] e28["-"] e29["-"]

a5["L"] j5["5"] l1["-"] l2["-"] l3["-"] l4["-"] l5["L"] l6["L"] l7["-"] l8["-"] l9["-"] l10["-"]
l11["-"] l12["-"] l13["-"] l14["-"] l15["-"] l16["-"] l17["-"] l18["-"] l19["-"] l20["-"]
l21["-"] l22["-"] l23["-"] l24["L"] l25["-"] l26["-"] l27["-"] l28["-"] l29["-"]

a6["G"] j6["6"] g1["-"] g2["-"] g3["-"] g4["-"] g5["-"] g6["-"] g7["-"] g8["G"] g9["-"] g10["-"]
g11["-"] g12["-"] g13["-"] g14["-"] g15["-"] g16["-"] g17["-"] g18["-"] g19["-"] g20["-"]
g21["-"] g22["-"] g23["-"] g24["-"] g25["-"] g26["-"] g27["-"] g28["-"] g29["-"]

a7["C"] j7["7"] c1["-"] c2["-"] c3["-"] c4["-"] c5["-"] c6["-"] c7["-"] c8["-"] c9["-"] c10["-"]
c11["C"] c12["-"] c13["-"] c14["-"] c15["-"] c16["-"] c17["-"] c18["-"] c19["-"] c20["-"]
c21["-"] c22["-"] c23["-"] c24["-"] c25["-"] c26["-"] c27["-"] c28["-"] c29["-"]

a8[" "] j8["8"] sp1["-"] sp2["-"] sp3["-"] sp4["-"] sp5["-"] sp6["-"] sp7["-"] sp8["-"] sp9["-"] sp10["-"]
sp11["-"] sp12["-"] sp13[" "] sp14["-"] sp15["-"] sp16[" "] sp17["-"] sp18["-"] sp19["-"] sp20[" "]
sp21["-"] sp22["-"] sp23["-"] sp24["-"] sp25["-"] sp26["-"] sp27["-"] sp28["-"] sp29["-"]

a9["B"] j9["9"] b1["-"] b2["-"] b3["-"] b4["-"] b5["-"] b6["-"] b7["-"] b8["-"] b9["-"] b10["-"]
b11["-"] b12["-"] b13["-"] b14["-"] b15["-"] b16["-"] b17["-"] b18["-"] b19["-"] b20["-"]
b21["-"] b22["B"] b23["-"] b24["-"] b25["-"] b26["-"] b27["-"] b28["-"] b29["-"]

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class t1,t2,t4,t5,t6,t7,t8,t9,t10 index
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class e1,e2,e3,e5,e6,e7,e8,e10 index
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class g1,g2,g3,g4,g5,g6,g7,g9,g10 index
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class c1,c2,c3,c4,c5,c6,c7,c8,c9,c10 index
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block-beta
columns 31

space:2 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"]

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s11["-"] s12["-"] s13["-"] s14["-"] s15["-"] s16["-"] s17["-"] s18["-"] s19["-"] s20["-"]
s21["-"] s22["-"] s23["-"] s24["-"] s25["-"] s26["-"] s27["-"] s28["-"] s29["-"]

a2["N"] j2["2"] n1["-"] n2["N"] n3["-"] n4["-"] n5["-"] n6["-"] n7["-"] n8["-"] n9["-"] n10["N"]
n11["-"] n12["-"] n13["-"] n14["-"] n15["-"] n16["-"] n17["-"] n18["-"] n19["-"] n20["-"]
n21["-"] n22["-"] n23["-"] n24["-"] n25["-"] n26["-"] n27["-"] n28["-"] n29["-"]

a3["T"] j3["3"] t1["-"] t2["-"] t3["T"] t4["-"] t5["-"] t6["-"] t7["-"] t8["-"] t9["-"] t10["-"]
t11["-"] t12["-"] t13["-"] t14["-"] t15["-"] t16["-"] t17["T"] t18["-"] t19["-"] t20["-"]
t21["-"] t22["-"] t23["-"] t24["-"] t25["-"] t26["T"] t27["-"] t28["-"] t29["T"]

a4["E"] j4["4"] e1["-"] e2["-"] e3["-"] e4["E"] e5["-"] e6["-"] e7["-"] e8["-"] e9["E"] e10["-"]
e11["-"] e12["E"] e13["-"] e14["-"] e15["-"] e16["-"] e17["-"] e18["-"] e19["-"] e20["-"]
e21["-"] e22["-"] e23["-"] e24["-"] e25["-"] e26["-"] e27["-"] e28["-"] e29["-"]

a5["L"] j5["5"] l1["-"] l2["-"] l3["-"] l4["-"] l5["L"] l6["L"] l7["-"] l8["-"] l9["-"] l10["-"]
l11["-"] l12["-"] l13["-"] l14["-"] l15["-"] l16["-"] l17["-"] l18["-"] l19["-"] l20["-"]
l21["-"] l22["-"] l23["-"] l24["L"] l25["-"] l26["-"] l27["-"] l28["-"] l29["-"]

a6["G"] j6["6"] g1["-"] g2["-"] g3["-"] g4["-"] g5["-"] g6["-"] g7["-"] g8["G"] g9["-"] g10["-"]
g11["-"] g12["-"] g13["-"] g14["-"] g15["-"] g16["-"] g17["-"] g18["-"] g19["-"] g20["-"]
g21["-"] g22["-"] g23["-"] g24["-"] g25["-"] g26["-"] g27["-"] g28["-"] g29["-"]

a7["C"] j7["7"] c1["-"] c2["-"] c3["-"] c4["-"] c5["-"] c6["-"] c7["-"] c8["-"] c9["-"] c10["-"]
c11["C"] c12["-"] c13["-"] c14["-"] c15["-"] c16["-"] c17["-"] c18["-"] c19["-"] c20["-"]
c21["-"] c22["-"] c23["-"] c24["-"] c25["-"] c26["-"] c27["-"] c28["-"] c29["-"]

a8[" "] j8["8"] sp1["-"] sp2["-"] sp3["-"] sp4["-"] sp5["-"] sp6["-"] sp7["-"] sp8["-"] sp9["-"] sp10["-"]
sp11["-"] sp12["-"] sp13[" "] sp14["-"] sp15["-"] sp16[" "] sp17["-"] sp18["-"] sp19["-"] sp20[" "]
sp21["-"] sp22["-"] sp23["-"] sp24["-"] sp25["-"] sp26["-"] sp27["-"] sp28["-"] sp29["-"]

a9["B"] j9["9"] b1["-"] b2["-"] b3["-"] b4["-"] b5["-"] b6["-"] b7["-"] b8["-"] b9["-"] b10["-"]
b11["-"] b12["-"] b13["-"] b14["-"] b15["-"] b16["-"] b17["-"] b18["-"] b19["-"] b20["-"]
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class g1,g2,g3,g4,g5,g6,g7,g8,g9,g10 hide
class g11,g12,g13,g14,g15,g16,g17,g18,g19,g20 hide
class g21,g22,g23,g24,g25,g26,g27,g28,g29 hide

class c1,c2,c3,c4,c5,c6,c7,c8,c9,c10 hide
class c11,c12,c13,c14,c15,c16,c17,c18,c19,c20 hide
class c21,c22,c23,c24,c25,c26,c27,c28,c29 hide

class sp1,sp2,sp3,sp4,sp5,sp6,sp7,sp8,sp9,sp10 hide
class sp11,sp12,sp13,sp14,sp15,sp16,sp17,sp18,sp19,sp20 hide
class sp21,sp22,sp23,sp24,sp25,sp26,sp27,sp28,sp29 hide

class b1,b2,b3,b4,b5,b6,b7,b8,b9,b10 hide
class b11,b12,b13,b14,b15,b16,b17,b18,b19,b20 hide
class b21,b22,b23,b24,b25,b26,b27,b28,b29 hide


class i1,i2,i3,i4,i5,i6,i7,i8,i9,i10 hide
class i11,i12,i13,i14,i15,i16,i17,i18,i19,i20 hide
class i21,i22,i23,i24,i25,i26,i27,i28,i29 hide

class j1,j2,j3,j4,j5,j6,j7,j8,j9 index

Mathematical Definition

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

Let \(CS\) is Congeneric Sequences

Let \(alphabet_p\) is Alphabet of partial sequence

Because by definition of Congeneric sequences \(\forall j \in \{1,...,m\}\) \(CS(j)\) is Congeneric sequence, so \(|alphabet_p(CS(j))| = 1\) because of Alphabet of Congeneric sequences lemma.

Define Alphabet of congeneric sequences function

\[alphabet_c : \big\{\{1,...,m\} \times \{1,...,l\} \longrightarrow X_{-} \big\} \longrightarrow \big\{\{1,...,m\} \longrightarrow X \big\},\]

\[alphabet_c(CS)(j) = alphabet_p(CS(j))(1)\]