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# User:Dmitry I. Ignatov

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Computer scientist working on Formal Concept Analysis (an applied branch of modern Lattice Theory aka Galois Lattices) and its applications in Machine Learning, Data Mining, Combinatorics and various applied domains.

Github: https://github.com/dimachine DBLP: https://dblp.org/pid/21/5524.html Google Scholar: https://scholar.google.com/citations?user=iExWnWsAAAAJ

My institution page: https://www.hse.ru/en/staff/dima .

## Some Related Papers

- On Shapley value interpretability in concept‐based learning with Formal Concept Analysis (co-authored by Leonard Kwuida)
- On the Cryptomorphism between Davis' Subset Lattices, Atomic Lattices, and Closure Systems under T1 Separation Axiom
- On Suboptimality of GreConD for Boolean Matrix Factorisation of Contranominal Scales (co-authored by Alexandra Yakovleva)
- On closure operators related to maximal tricliques in tripartite hypergraphs

## Contribution to Sequences

- A326359 Number of maximal antichains of nonempty subsets of {1..n}.
- A326360 Number of maximal antichains of nonempty, non-singleton subsets of {1..n}.
- A334255 Number of strict closure operators on a set of n elements which satisfy the T_1 separation axiom.
- A334254 Number of closure operators on a set of n elements which satisfy the T_1 separation axiom.
- A305233 Smallest k such that binomial(k, floor(k/2)) >= n. (comments and references only)
- A235604 Number of equivalence classes of lattices of subsets of the power set 2^[n].
- A055869 Number of switching generators for a power polyadic n-context ({1..k}, ..., {1..k}, <>) with n=k. See paper in DAM.

## Original Sequences

- A348260 Number of inequivalent maximal antichains of the Boolean lattice on a set of n elements.
- A349481 a(n) is the number of Boolean factors of the contranominal scale of size n by the GreConD algorithm for Boolean matrix factorization.
- A355517 Number of nonisomorphic systems enumerated by A334254; that is, the number of inequivalent closure operators on a set of n elements where all singletons are closed.
- A358041 The number of maximal antichains in the lattice of set partitions of an n-element set.
- A358390 The number of maximal antichains in the Kreweras lattice of non-crossing set partitions of an n-element set.
- A358391 The number of antichains in the Kreweras lattice of non-crossing set partitions of an n-element set.
- A358562 The number of antichains in the Tamari lattice of order n.
- A358563 The number of maximal antichains in the Tamari lattice of order n.