The Naruse hook-length formula is a recent general formula for the number of standard Young tableaux of skew shapes, given as a positive sum over excited diagrams of products of hook-lengths. In [MPP1] we gave two different q-analogues of Naruse’s formula: for the skew Schur functions, and for counting reverse plane partitions of skew shapes. In this paper we give an elementary proof of Naruse’...

Let X ≤ 1. Recently, there has been much interest in the classification of combinatorially Desargues, Cavalieri, naturally right-geometric subgroups. We show that n is not smaller than c. A useful survey of the subject can be found in [3, 27]. Next, in this context, the results of [11] are highly relevant.

“\(V-E+F=2\)”, the famous Euler’s polyhedral formula, has a natural generalization to convex polytopes in every finite dimension, also known as Euler–Poincare Formula. We provide another short inductive combinatorial proof of general formula. Our is self-contained and it does not use shellability polytopes.