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Polynomial identities for partitions
European Journal of Combinatorics, 1992 Set \(P_ 1(q)=1-q\) and \(P_ k(q)=\sum_{d\mid k}\mu(k/d)\) for \(k>1\). For every integer \(m>1\) define \[ P^ +_{k,m}(q)=P_ k(q)(P_ k(q)+k)(P_ k(q)+2k)\cdots(P_ k(q)+(m-1)k), \] \[ P^ -_{k,m}(q)=P_ k(q)(P_ k(q)-k)(P_ k(q)-2k)\cdots(P_ k(q)-(m-1)k); \] and set \(P^ +_{k,0}(q)=P^ -_{k,0}(q)=1\).
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MacWilliams Identities and Matroid Polynomials [PDF]
The Electronic Journal of Combinatorics, 2002 We present generalisations of several MacWilliams type identities, including those by Kløve and Shiromoto, and of the theorems of Greene and Barg that describe how the Tutte polynomial of the vector matroid of a linear code determines the $r$th support weight enumerators of the code.
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Annals of Combinatorics / Elementary polynomial identities involving q-trinomial coefficients [PDF]
, 2019 We use the q-binomial theorem to prove three new polynomial identities involving q-trinomial coefficients. We then use summation formulas for the q-trinomial coefficients to convert our identities into another set of three polynomial identities, which imply ...
Uncu, Ali Kemal, Berkovich, Alexander
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On the *-polynomial identities of M_{1;1}(E)
, 2011 In this paper we consider the algebra M_{1,1}(E) endowed with the involution ∗ induced by the transposition superinvolution of the superalgebra M_{1,1}(F ) of 2 × 2-matrices over the field F . We study the ∗-polynomial identities for this algebra in the
P. KOSHLUKOV +5 more
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Generalized monotone triangles [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 In a recent work, the combinatorial interpretation of the polynomial $\alpha (n; k_1,k_2,\ldots,k_n)$ counting the number of Monotone Triangles with bottom row $k_1 < k_2 < ⋯< k_n$ was extended to weakly decreasing sequences $k_1 ≥k_2 ≥⋯≥k_n$.
Lukas Riegler
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Generalized Pseudospectral Method and Zeros of Orthogonal Polynomials
Advances in Mathematical Physics, 2018 Via a generalization of the pseudospectral method for numerical solution of differential equations, a family of nonlinear algebraic identities satisfied by the zeros of a wide class of orthogonal polynomials is derived.
Oksana Bihun, Clark Mourning
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Irreducible polynomial identities in anticommutative algebras
, 1970 The methods introduced by J. M. Osborn for isolating those polynomial identities worth studying in commutative algebras are here modified to yield three theorems for anticommutative algebras.
Seymour Kass, William G. Witthoft
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Homogeneous involution on graded division algebras and their polynomial identities
, 2022 In this short note, we describe the so-called homogeneous involution on finite-dimensional graded-division algebra over an algebraically closed field. We also compute their graded polynomial identities with involution. As pointed out by L. Fonseca and T.
Yasumura, Felipe Yukihide +1 more
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Attaching a matrix algebra to affine group schemes: Polynomial identities
, 2023 We give a definition of polynomial identities for affine group schemes; over a field F of characteristic 0, the identities of an affine group scheme turn out to coincide with the identities of a certain matrix algebra over F.
Lucio Centrone
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Ligand‐dependent transcriptional heterogeneity in cell cycle gene expression delays G1/S entry
FEBS Letters, EarlyView.EGF and HRG induce distinct G1/S progression programs in ErbB2‐amplified BT474 breast cancer cells. Despite activating the potent ErbB2–ErbB3 heterodimer, HRG does not accelerate cell‐cycle entry. Instead, EGF promotes earlier restriction‐point passage via ERK–FOS signaling, whereas HRG activates the AKT–MYC axis, driving transcriptional heterogeneity ...
Ririn Rahmala Febri +5 more
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