## 3 Results  
Tables 1 and 2 present the distributions of fractional credit shares from \(n=2\) to 15 using the values of \(k\) equal to 0.2 and 0.4, respectively. All the rows of the tables show uniformly decreasing credit shares while moving rightward from the first author to the last. All the  
shares in a row finally add up to 1, as shown in the last columns of the tables. Moreover, it can also be observed that the share of the first author decreases as the number of coauthors increases but it always remains more than the other coauthors. It is also worthwhile to note that the coauthor at the mid position of an authors list presented as an odd numbered row (\(n=3,5,7,\dots\)) of Table 1 (\(k=0.2\)) holds exactly the same fractional credit share as the one in the same row of Table 2 (\(k=0.4\)). This holds true for the higher values of \(k\), too. Thus, it can be inferred that the uniform spread of the fractional credit shares among a given number of coauthors is centered at the middle of the authors list. These observations speak of the fairness and correctness of the proposed method in dividing a publication's credit among its multiple coauthors.  
Table 3 presents the differences and percentage differences between the fractional credit shares of the first and the last authors regarding the cases of two and 15 coauthors per publication, with the value of \(k\) varying from 0 to 1.2 at an increment of 0.2. It is observable that an increase in the value of \(k\) raises the difference between the shares of the first and the last authors for \(n=2\) as well as \(n=15\). Understandably, the absolute values are higher for  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\(n\)} & \multicolumn{8}{c}{**Sequence Number of the Researcher in Authors List (\(j\))**} & \multirow{2}{*}{**Sum**} \\ \cline{2-13}  & & & & & & & & & & & & & & & \\ \hline
2 & 0.550 & 0.450 & - & - & - & - & - & - & - & - & - & - & - & - & - & 1 \\
3 & 0.367 & 0.333 & 0.300 & - & - & - & - & - & - & - & - & - & - & - & - & 1 \\
4 & 0.275 & 0.258 & 0.242 & 0.225 & - & - & - & - & - & - & - & - & - & - & - & - & 1 \\
5 & 0.220 & 0.210 & 0.200 & 0.190 & 0.180 & - & - & - & - & - & - & - & - & - & - & - & - & 1 \\
6 & 0.183 & 0.177 & 0.170 & 0.163 & 0.157 & 0.150 & - & - & - & - & - & - & - & - & - & - & 1 \\
7 & 0.157 & 0.152 & 0.148 & 0.143 & 0.138 & 0.133 & 0.129 & - & - & - & - & - & - & - & - & - & 1 \\
8 & 0.138 & 0.134 & 0.130 & 0.127 & 0.123 & 0.120 & 0.116 & 0.113 & - & - & - & - & - & - & - & - & 1 \\
9 & 0.122 & 0.119 & 0.117 & 0.114 & 0.111 & 0.108 & 0.106 & 0.103 & 0.100 & - & - & - & - & - & - & - & 1 \\
10 & 0.110 & 0.108 & 0.106 & 0.103 & 0.101 & 0.099 & 0.097 & 0.094 & 0.092 & 0.090 & - & - & - & - & - & 1 \\
11 & 0.100 & 0.098 & 0.096 & 0.095 & 0.093 & 0.091 & 0.089 & 0.087 & 0.085 & 0.084 & 0.082 & - & - & - & - & 1 \\
12 & 0.092 & 0.090 & 0.089 & 0.087 & 0.086 & 0.084 & 0.083 & 0.081 & 0.080 & 0.078 & 0.077 & 0.075 & - & - & - & 1 \\
13 & 0.085 & 0.083 & 0.082 & 0.081 & 0.079 & 0.078 & 0.077 & 0.076 & 0.074 & 0.073 & 0.072 & 0.071 & 0.069 & - & - & 1 \\
14 & 0.079 & 0.077 & 0.076 & 0.075 & 0.074 & 0.073 & 0.072 & 0.071 & 0.070 & 0.069 & 0.068 & 0.066 & 0.065 & 0.064 & - & 1 \\
15 & 0.073 & 0.072 & 0.071 & 0.070 & 0.070 & 0.069 & 0.068 & 0.067 & 0.066 & 0.065 & 0.064 & 0.063 & 0.062 & 0.061 & 0.060 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Uniformly decreasing distribution of fractional credit shares of a publication among the coauthors (2–15). \(k=0.2\).  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\(n\)} & \multicolumn{8}{c}{**Sequence Number of the Researcher in Authors List (\(j\))**} & \multirow{2}{*}{**Sum**} \\ \cline{2-13}  & & & & & & & & & & & & & & & & \\ \hline
2 & 0.6 & 0.4 & - & - & - & - & - & - & - & - & - & - & - & - & - & 1 \\
3 & 0.400 & 0.333 & 0.267 & - & - & - & - & - & - & - & - & - & - & - & - & - & 1 \\
4 & 0.30