We present a version of the weighted cellular matrix-tree theorem that is suitable for calculating explicit generating functions for spanning trees of highly structured families of simplicial and cell complexes. We apply the result to give weighted generalizations of the tree enumeration formulas of Adin for complete colorful complexes, and of Duval, Klivans and Martin for skeleta of hypercubes...

MacMahon’s classic theorem states that the length and major index statistics are equidistributed on the symmetric group Sn. By defining natural analogues or generalizations of those statistics, similar equidistribution results have been obtained for the alternating group An by Regev and Roichman, for the hyperoctahedral group Bn by Adin, Brenti and Roichman, and for the group of even-signed per...

We study the coinvariant ring of the complex reflection group G(r, p, n) as a module for the corresponding rational Cherednik algebra H and its generalized graded affine Hecke subalgebra H. We construct a basis consisting of non-symmetric Jack polynomials, and using this basis decompose the coinvariant ring into irreducible modules forH. The basis consists of certain non-symmetric Jack polynomi...

Five trials investigated the feeding value of wet and dried corn distillers byproducts as a source of protein and energy for growing and finishing cattle and investigated the effect of heat damage on the feeding value of dried distillers byproducts. In a calf growth trial, no differences in rate of gain or protein efficiency were observed among calves fed wet distillers byproducts (wet distille...

Pharmacognosy Research,2023,15,1,145-154.DOI:10.5530/097484900241Published:December 2022Type:Original ArticleAuthors:Isha Gupta, Syeda Nashvia Adin, Mohd Aqil, and Mujeeb Author(s) affiliations:Isha Gupta1,#, Adin1,#, Aqil2,*, Mujeeb1,* 1Phytomedicine Laboratory, Department of Phytochemistry, School Pharmaceutical Education Research, Jamia Hamdard, New Delhi, INDIA. 2Department Pharmaceutics, #...

Given a permutation π ∈ Sn, let Γ−(π) be the graph on n vertices {1, . . . , n} where two vertices i < j are adjacent if π(i) > π(j) and there are no integers k, i < k < j, such that π(i) > π(k) > π(j). Let Γ(π) be the graph obtained by dropping the condition that π(i) > π(j), i.e. two vertices are adjacent if the rectangle [i, π(i)] × [j, π(j)] is empty. In the study of the strong order on per...