Results 41 to 50 of about 980 (86)
The combinatorial structure of trigonometry
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 8, Page 475-500, 2003., 2003 The native mathematical language of trigonometry is combinatorial. Two interrelated combinatorial symmetric functions underlie trigonometry. We use their characteristics to derive identities for the trigonometric functions of multiple distinct angles.
Adel F. Antippa
wiley +1 more source
A short proof of an identity of Sylvester
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 2, Page 431-435, 1999., 1999 We present two short proofs of an identity found by Sylvester and rediscovered by Louck. The first proof is an elementary version of Knuth′s proof and is analogous to Macdonald′s proof of a related identity of Milne. The second is Sylvester′s own proof of his identity.
Gaurav Bhatngar
wiley +1 more source
Delta and Theta Operator Expansions
Forum of Mathematics, SigmaWe give an elementary symmetric function expansion for the expressions $M\Delta _{m_\gamma e_1}\Pi e_\lambda ^{\ast }$ and $M\Delta _{m_\gamma e_1}\Pi s_\lambda ^{\ast }$ when $t=1$ in terms of what we call $\gamma $ -parking ...
Alessandro Iraci, Marino Romero
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Schur convexity for the ratios of the Hamy and generalized Hamy symmetric functions
, 2011 In this paper, we present the Schur convexity and monotonicity properties for the ratios of the Hamy and generalized Hamy symmetric functions and establish some analytic inequalities. The achieved results is inspired by the paper of Hara et al.
Wei-Mao Qian
semanticscholar +1 more source
A raising operator formula for Macdonald polynomials
Forum of Mathematics, SigmaWe give an explicit raising operator formula for the modified Macdonald polynomials $\tilde {H}_{\mu }(X;q,t)$ , which follows from our recent formula for $\nabla $ on an LLT polynomial and the Haglund-Haiman-Loehr formula expressing ...
J. Blasiak +4 more
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DUAL EQUIVALENCE GRAPHS I: A NEW PARADIGM FOR SCHUR POSITIVITY
Forum of Mathematics, Sigma, 2015 We make a systematic study of a new combinatorial construction called a dual equivalence graph. We axiomatize these graphs and prove that their generating functions are symmetric and Schur positive.
SAMI H. ASSAF
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Veterinary Dermatology, EarlyView.Background – Inhibition of the Janus kinase (JAK) pathway is a well‐established option for canine atopic dermatitis (cAD). Objective – To evaluate the efficacy and safety of ilunocitinib, a novel JAK inhibitor for the control of pruritus and skin lesions in client‐owned dogs with cAD.
Sophie Forster +5 more
wiley +1 more source
Schubert polynomial expansions revisited
Forum of Mathematics, SigmaWe give an elementary approach utilizing only the divided difference formalism for obtaining expansions of Schubert polynomials that are manifestly nonnegative, by studying solutions to the equation $\sum Y_i\partial _i=\operatorname {id}$ on ...
Philippe Nadeau +2 more
doaj +1 more source
Thom Polynomials and Schur Functions: The Singularities A3(−)
, 2010 Combining the “method of restriction equations” of Rimányi et al. with the techniques of symmetric functions, we establish the Schur function expansions of the Thom polynomials for the Morin singularities A3 : (C•, 0)→ (C•+k, 0) for any nonnegative ...
A. Lascoux, P. Pragacz
semanticscholar +1 more source
Veterinary Dermatology, Volume 35, Issue 6, Page 595-604, December 2024.Background – Mycobacterium cell wall fraction (MCWF) is derived from nonpathogenic Mycobacterium phlei and is used as an immunomodulatory compound in clinical practice, yet its mode‐of‐action requires further research. Objective – To evaluate the host response to MCWF in canine peripheral blood mononuclear cells (PBMCs) by using enzyme‐linked ...
Robert Ward +9 more
wiley +1 more source