Noncommutative symmetric functions of type B

By Chak-On Chow. 2001

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Enriched P-partitions and peak algebras (2005, methodology): “Theorem 2.9 (Chow [14]).”
The peak algebra and the descent algebras of types B and D (2003, background): “(4) More information on the commutative subalgebra s ( B n ) of Section 6.1 can be found in Chow’s thesis [12, Sections 4.2, 4.3 and 5.1].”
Recent Trends in Quasisymmetric Functions (2018, background): “A number of very interesting subtopics are therefore excluded from this article, including Stembridge’s subalgebra of peak quasisymmetric functions [122] and its associated structure ([16], [17], [19], [20], [34], [81]), Ehrenborg’s flag quasisymmetric function of a partially ordered set [34], color”
Advanced Determinant Calculus: A Complement (2005, background): “X + j)*(-4)∧k; f1[k , t , j ] := -(4*4*k*(4*k + 1) - 4*X + 2 + 4*j)*(-4)∧k; g0[k , t , j ] := (X - j); g1[k , t , j ] := (-4*X + 2 + 4*j) and let us compute the new determinant for k = 2: In[31]:= Factor[Det[A[2]]] This makes us wait for another 15 minutes, after which we are rewarded with: Out[31]=”