On the Hadamard product of Hopf monoids

Combinatorial structures which compose and decompose give rise to Hopf monoids in Joyal's category of species. The Hadamard product of two Hopf monoids is another Hopf monoid. We prove two main results regarding freeness of Hadamard products. The first one states that if one factor is connected and the other is free as a monoid, their Hadamard product is free (and connected). The second provides an explicit basis for the Hadamard product when both factors are free. The first main result is obtained by showing the existence of a one-parameter deformation of the comonoid structure and appealing to a rigidity result of Loday and Ronco which applies when the parameter is set to zero. To obtain the second result, we introduce an operation on species which is intertwined by the free monoid functor with the Hadamard product. As an application of the first result, we deduce that the dimension sequence of a connected Hopf monoid satisfies the following condition: except for the first, all coefficients of the reciprocal of its generating function are nonpositive

“’Chinese don’t drink coffee!’”: Coffee and Class Liminality in Elaine Mar’s Paper Daughter

This article offers a reading of the foodservice spaces in Elaine Mar’s memoir Paper Daughter in order to suggest changes in the way we think about class liminality. It argues that by focusing not just on the way the socially-mobile narrator experiences liminality, but also on the ways her working-class parents and co-workers experience it, we can begin to consider some of the complexities and nuances the idea of the liminal offers. In so doing, the article suggests a slightly new approach to thinking about and teaching Paper Daughter

Hopf monoids from class functions on unitriangular matrices

We build, from the collection of all groups of unitriangular matrices, Hopf monoids in Joyal's category of species. Such structure is carried by the collection of class function spaces on those groups, and also by the collection of superclass function spaces, in the sense of Diaconis and Isaacs. Superclasses of unitriangular matrices admit a simple description from which we deduce a combinatorial model for the Hopf monoid of superclass functions, in terms of the Hadamard product of the Hopf monoids of linear orders and of set partitions. This implies a recent result relating the Hopf algebra of superclass functions on unitriangular matrices to symmetric functions in noncommuting variables. We determine the algebraic structure of the Hopf monoid: it is a free monoid in species, with the canonical Hopf structure. As an application, we derive certain estimates on the number of conjugacy classes of unitriangular matrices.Comment: Final Version, 32 pages, accepted in "Algebra and Number Theory

The effects of freezing and storage time on the quality of reindeer meat

Master's Project University of Alaska Fairbanks, 2017Restaurants, wholesalers and retailers of fresh meat require a year round consistent supply of uniform quality product to sustain demand and justify niche market costs such as advertisement and stocking product. Frozen reindeer meat could be stored, short or long term to increase availability provided there are no adverse effects of freezing. No studies to date have evaluated the effects of freezing and storage time on reindeer meat quality. Nine reindeer steers (castrated bulls; age 2.5 years) were fed a balanced milled ration at the University of Alaska Fairbanks (UAF) Reindeer Research Program (RRP) facility at the Agricultural Forestry Experiment Station (AFES). In February, animals were transported to a USDA approved meat processing facility for slaughter where both striploins (M. longissimus dorsi) were removed from the carcasses. The striploin samples were allocated to four subsamples consisting of fresh (control), freshly frozen, 6 month frozen and 12 month frozen treatment groups to determine if freezing and frozen storage of reindeer meat for up to one year effects meat quality. All samples underwent shear force measurement, water holding capacity (WHC) determination, proximate analysis, sensory evaluation, TBARS (rancidity) and fatty acid methyl ester profile (FAMES) analysis. Meat was sampled after 6 months of frozen storage for amino acid and mineral analysis. Shear force values were not significantly different amongst treatment groups fresh to 12 month (P=0.992). Purge and cooking loss variation were significant between fresh and 12 months (P = 1e-05,1e-04). There was no significant difference from fresh to 12 month in moisture, ash and protein content while lipid content variation was significantly different (P = 0.99, 1.00, 1.00 and < 1e -6 respectively). Tenderness and juiciness attributes were not significantly different among treatment groups fresh and 12 month (P=0.91 and P=0.53); however, an off flavor attribute was significantly different (P=0.005) amongst treatment groups suggesting that off flavor diminishes with freezing. While not detected in sensory evaluation, mean TBARS (rancidity) values increased significantly (P = <.1e-04) between fresh and 12 months. Characterization of reindeer muscle indicated that the amino acid profile and selected mineral were consistent with that of a high quality nutritional meat product. Omega 3 fatty acid (W3), Omega 6 fatty acid (W6), Monounsaturated fatty acid (MUFA), Polyunsaturated fatty acid (PUFA), the ratio between Omega 3 and Omega 6 (W3/W6) and the ratio between PUFA and MUFA (PS) were not significantly different while Saturated fatty acid (SAFA) was significantly different amongst treatments groups from fresh to 12 months. (P= 0.35, 1.00, 0.96, 0.12, 1.00, 0.14 and 0.03). Results of this study suggest reindeer meat can be frozen for up to a year without compromising quality. This could facilitate the marketing flexibility for the reindeer industry to be able to provide a consistent supply of product year round to niche restaurants and wholesalers while commanding a premium price