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We obtain a necessary and sufficient condition for the linear independence of solutions of differential equations for hyperlogarithms. The key fact is that the multiplier (i.e. the factor $M$ in the differential equation $dS=MS$) has only singularities of first order (Fuchsian-type equations) and this implies that they freely span a space which contains no primitive. We give direct applications where we extend the property of linear independence to the largest known ring of coefficients.
On complex algebraic varieties, height functions arising in combinatorial applications fail to be proper. This complicates the description and computation via Morse theory of key topological invariants. Here we establish checkable conditions under wh
We first formulate a function field version of Vojtas generalized abc conjecture for algebraic tori. We then show a function field analogue of the Lang-Vojta Conjecture for varieties of log general type that are ramified covers of $mathbb G_m^n$. In
We consider the algebraic combinatorics of the set of injections from a $k$-element set to an $n$-element set. In particular, we give a new combinatorial formula for the spherical functions of the Gelfand pair $(S_k times S_n, text{diag}(S_k) times S
Building upon the rule-algebraic stochastic mechanics framework, we present new results on the relationship of stochastic rewriting systems described in terms of continuous-time Markov chains, their embedded discrete-time Markov chains and certain ty
This note is purely expository and is in Russian. We show how to prove interesting combinatorial results using the local Lovasz lemma. The note is accessible for students having basic knowledge of combinatorics; the notion of independence is defined