I-Wilf Inversion Sequences In [a] introduced an algorithmic approach (KMY) based on a generating tree method for enumerating the inversion sequences with various pattern-avoidance restrictions. For a given set of patterns, we propose an algorithm that outputs either an accurate description of the succession rules of the corresponding generating tree or an ansatz. By using this approach, we determine the generating trees for the pattern classes I_n(B) (the set of inversion sequences of length n that avoid a set of patterns B).

In [b] applied KMY-algorithm to bounded the number I-Wilf-equivalence classes of sets of three length-3 patterns.

In [c] applied KMY-algorithm to bounded the number I-Wilf-equivalence classes of sets of four length-3 patterns.

As next step, we present the data that is needed to find all I-Wilf-equivalence classes of sets of d length-3 patterns, d=5,6,7,8,9,10,11,12,13.
Step 1: For any set of d length-3 patterns B, find the number of inversion sequences in I_n(B), for n=0,1,...,9. We present the output as a table of binomial(13,d) lines such that each line has the form (|I_0(B)|,...,|I_9(B)|). By sorting this table respect with to the sequences (|I_0(B)|,...,|I_9(B)|) and separating different sequences by a space line, we complete the first step. Here, we call this table by d-sorted table, see InvSeqDataSorted[5].txt, InvSeqDataSorted[6].txt, InvSeqDataSorted[7].txt, InvSeqDataSorted[8].txt, InvSeqDataSorted[9].txt, InvSeqDataSorted[10].txt, InvSeqDataSorted[11].txt, InvSeqDataSorted[12].txt, InvSeqDataSorted[13].txt.
Step 2: For any set of patterns B in the file InvSeqDataSorted[d].txt, we apply generating trees step for finding GT_ell(B) (with small ell). The output of all GT_ell(B) with B\in P_d (P_d is the set of all subsets of d length-3 patterns) is stored in a pdf file called InvSeqAvoid[d]pat3pdf.pdf, see InvSeqAvoid[5]pat3pdf.pdf, InvSeqAvoid[6]pat3pdf.pdf, InvSeqAvoid[7]pat3pdf.pdf, InvSeqAvoid[8]pat3pdf.pdf, InvSeqAvoid[9]pat3pdf.pdf, InvSeqAvoid[10]pat3pdf.pdf, InvSeqAvoid[11]pat3pdf.pdf, InvSeqAvoid[12]pat3pdf.pdf, (there is no need a such table for d=13).
Step 3: Let w_d be the number of distinct I-Wilf-equivalence classes of sets of d length-3 patterns.. We show that w_5=219, w_6=167, w_7=105, w_8=61, w_9=35, w_10=21, w_11=10, w_12=4, and w_13=1.

References:
[a] I. Kotsireas, T. Mansour and G. Yildirim, An algorithmic approach based on generating trees for enumerating pattern-avoiding inversion sequences, Journal of Symbolic Computation 120 (2024), Article 102231.
[b] D. Callan, V. Jelinek, and T. Mansour, Inversion sequences avoiding a triple of patterns of 3 letters, Electronic Journal of Combinatorics 30:3 (2023), #P3.19.
[c] D. Callan and T. Mansour, Inversion sequences avoiding a quadruple length-3 patterns, Integers: Electronic Journal of Combinatorial Number Theory 23 (2023), #A78.