Dear Guys,

Excellent paper, Pawel (clear, pedagogical and deep). Below some (few) 
suggestions for improvement.

Best regards
Gérard

PS: I didn't put line?, please tell me if the sheet is OK.
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Abstract

[From this starting point we explore combinatorial]-->
[From this starting point, we explore combinatorial]

Introduction

[where I is multiplicative identity.]-->
[where I is the (unique) multiplicative identity.]

Heisenberg–Weyl algebra

[associative algebra with the unit]-->
[associative algebra with unit]
sorry, I didn't notice this previously (see Algebras and rings in the following)
http://en.wikipedia.org/wiki/Algebra_over_a_field

3.3. Combinatorial realization of the Heisenberg–Weyl algebra

[With this equivalence the algebraic structure of H and its]-->
[With this equivalence, the algebraic structure of H and its]

References

[17] [agentle]-->[a gentle]